Electromagnetic Waves: Class 12 Physics Chapter 8 Hinglish mein

Physics Part 1 · Hinglish notes, simulations aur practice · Official NCERT chapter PDF ↗

Published 12 Oct 2026 · Updated 12 Oct 2026

95 min
17 practice questions
27 MCQs

Is chapter mein aap kya seekhenge

Samjho ki charging capacitor ke liye Ampère's circuital law kyun fail hota hai, aur Maxwell ka displacement current is contradiction ko kaise hatata hai
Displacement currents aur unse bane magnetic fields calculate karo, charging capacitor ki plates ke beech ka field bhi
Maxwell ke chaar equations integral form mein likho, aur batao ki har ek electric aur magnetic fields ke sources ke baare mein kya kehta hai
Samjho ki accelerated charges electromagnetic waves kaise banate hain, aur Hertz, J. C. Bose aur Marconi ke experiments describe karo
Plane electromagnetic wave describe karo, jismein perpendicular electric aur magnetic fields same phase mein hote hain, aur E0 = cB0, c = 1/√(μ0ε0) aur v = 1/√(με) use karo
k = 2π/λ, ω = 2πν aur c = νλ use karke E aur B ke wave equations likho aur samjho, aur fields jo energy le jaate hain woh nikaalo
Electromagnetic spectrum ke regions ko order mein batao, unki rough wavelength ranges, sources, detectors, uses aur hazards ke saath
Photon energy ko frequency se jodo, aur samjho ki spectrum ke alag-alag regions matter ke saath itna alag interact kyun karte hain

NCERT Physics Class 12, Chapter 8, pp. 201–214 par based original companion text. Yeh NCERT se juda nahi hai aur NCERT ne ise endorse nahi kiya hai.

8.1 Introduction

Ek phone uthao. Mobile tower aur Wi-Fi router ke signals us tak pahunch rahe hain, uski screen tumhari aankhon tak light bhej rahi hai, aur khidki se aati sunlight tumhara haath garam kar rahi hai. Hospital scanner ke X-rays aur cancer ke treatment mein use hone wali gamma rays bhi isi family ki hain. Yeh sab electromagnetic waves (वैद्युतचुंबकीय तरंगें) hain: electric aur magnetic field ke chalte hue patterns jo sirf wavelength mein alag hain. Yeh chapter samjhata hai ki aisi wave kya hoti hai, Maxwell ne kisi ke banane se pehle hi paper par iska prediction kaise kiya, aur poori family ko ek spectrum mein kaise arrange kiya jaata hai.

In waves tak ka raasta capacitor ki ek chhoti si puzzle se shuru hota hai. Use charge kar rahi wire par Ampère's circuital law lagao, to answer is baat par depend karta hai ki tumne kaunsi surface draw ki, aur nature ka koi law aisa kabhi nahi kar sakta (Section 8.2). Maxwell ka ilaaj yeh tha ki time ke saath badalte electric field ko bhi magnetic field ka source maana jaaye, bilkul current ki tarah. Is naye term ko unhone displacement current kaha. Fig. 8.1 dikhata hai ki yeh ek addition itna important kyun hai: yeh dono fields ke beech cause aur effect ka loop poora kar deta hai.

3/4Maxwell ka naya link: time ke saath badalta electric field ek magnetic field banata hai.

Fig. 8.1Charges aur currents fields banate hain; changing fields ek doosre ko banate hain. Aakhri link Maxwell ne joda, aur isse fields khud se travel kar sakte hain.NCERT p. 201

Do circles aamne-saamne hain: left mein electric field E ke liye ek orange circle aur right mein magnetic field B ke liye ek blue circle. Step 1: bilkul left mein charges likha ek box E ki taraf orange arrow bhejta hai, aur bilkul right mein currents likha ek box B ki taraf blue arrow bhejta hai; dono circles judte nahi. Step 2: circles ke neeche ek orange arc, jis par changing B aur Faraday, 1831 likha hai, B se E tak jaata hai. Step 3: unke upar ek blue arc, jis par changing E aur Maxwell, 1862 likha hai, E se B tak jaata hai. Step 4: charges aur currents wale boxes halke pad jaate hain, dono arcs mote hokar loop mein ghoomte hain, aur neeche speed c likha ek wavy arrow dikhata hai ki fields ka pair wave ban kar door jaata hai.

Loop poora hone par dono fields kisi bhi charge ya current se door ek doosre ko chalate reh sakte hain. Changing $𝐄$ ek changing $𝐁$ ko banaye rakhta hai, aur woh changing $𝐁$ badle mein changing $𝐄$ ko banaye rakhta hai. Maxwell's equations, yaani Table 8.1 ke chaar laws, predict karte hain ki aisa disturbance $1 / \sqrt{μ_{0} ε_{0}}$ speed se travel karta hai. Dono constants charges aur currents ke bench experiments se aate hain, phir bhi result $3.00 \times 10^{8} m / s$ aata hai. 1849 mein Hippolyte Fizeau ne Paris ke paas $17 k m$ ke round trip par light ki beam ka time naapa tha aur lagbhag $3.15 \times 10^{8} m / s$ paaya tha. Is match se Maxwell ko yakeen ho gaya ki light ek electromagnetic wave hai, aur optics electromagnetism ka hissa ban gaya.

Is prediction ko test hone mein do dashak lag gaye. 1887 mein Heinrich Hertz ne apni laboratory mein electromagnetic waves banayi aur detect ki, aur radio, radar, television aur mobile phones unhi ke apparatus se nikle. Hum displacement current se shuru karte hain, phir dekhte hain ki waves kaise launch hoti hain aur dikhti kaisi hain. Chapter spectrum ke tour ke saath khatam hota hai, metre ke trillionth hisse se bhi chhoti gamma rays se lekar kai kilometre lambi radio waves tak.

History seNCERT p. 202

James Clerk Maxwell (1831–1879)

Maxwell Edinburgh mein paida hue aur chaudah saal ki umar mein apna pehla scientific paper likha, oval curves draw karne ke ek tareeke par. Unhone dikhaya ki Saturn ke rings solid nahi ho sakte, woh anginat chhoti bodies se bane hone chahiye. Unhone yeh bhi nikaala ki gas mein molecules ki speeds kaise distributed hoti hain, aur 1861 mein red, green aur blue images ko milakar pehli colour photograph project ki. 1861 aur 1865 ke beech unhone Coulomb, Gauss, Ampère aur Faraday ke laws ko ek saath joda. Unhone displacement current joda aur A Dynamical Theory of the Electromagnetic Field mein light ki speed se travel karne wali waves ka prediction kiya. 48 saal ki umar mein unki death ho gayi, Hertz ke prediction confirm karne se aath saal pehle.

Warm-up

2 mein se 1

Oersted, Ampère aur Faraday jo pehle hi dhoondh chuke the, usmein Maxwell ne electric aur magnetic fields ke beech kaunsa link joda?

Electric current magnetic field banata haiChanging magnetic field electric field banata haiChanging electric field magnetic field banata haiSteady electric field steady magnetic field banata hai

Answer dekho

Answer (C) Changing electric field magnetic field banata hai

Currents se magnetic fields banna (Oersted, Ampère) aur changing magnetic fields se electric fields banna (Faraday) unse pehle hi pata tha. Maxwell ka naya idea Faraday ka ulta tha: changing electric field magnetic field banata hai. Steady electric field koi magnetic field nahi banata.

8.2 Displacement current

Chapter 4 ka Ampère's circuital law closed loop ke around magnetic field ko loop se guzarne wale current se jodta hai:

Ampère's circuital law

\oint 𝐁 \cdot d 𝐥 = μ_{0} i (t)

(8.1)

jahan

$i (t)$: kisi bhi aisi surface se current jiski boundary yeh loop hai

Kisi bhi surface wale shabd important hain. Ek loop anginat surfaces ka rim hota hai: flat disc, halka dome, gehra bag. Law kehta hai ki in sab se same current guzarta hai. Wire mein steady current ke liye yeh sach hai, kyunki charge kahin jama nahi ho sakta; kisi closed region mein jo andar aata hai woh bahar bhi nikal jaata hai. Maxwell ne poocha ki jab charge sach mein jama hota hai tab kya hota hai, jaise capacitor ko charge karte waqt uski plates par hota hai.

Ampère's law do choices maangta hai: ek closed loop, aur ek surface jiska edge woh loop ho. Yeh choices Fig. 8.2 ke capacitor ke liye karo, jo seedhi wire mein upar behte current $i (t)$ se charge ho raha hai. Loop ke liye wire par centred, radius $r$ ka ek horizontal circle lo, lower plate se thoda neeche. Apparatus ko wire ke around ghumane se kuch nahi badalta, isliye field is circle ke around ek hi strength $B$ ke saath lipta hona chahiye. Tab (8.1) ka left side $2 π r B$ ban jaata hai. Surface ke liye seedha choice flat disc $S_{1}$ hai jo circle ko bharti hai. Wire ise cheerti hai, isliye

B (2 π r) = μ_{0} i (t)

(8.2)

Ab same loop rakho lekin balloon jaisi surface $S_{2}$ lo, jo loop se upar uthti hai, lower plate ke around jaati hai aur plates ke beech gap mein band hoti hai. $S_{2}$ ko kahin bhi koi wire cross nahi karti, isliye usse current zero hai, aur Ampère's law usi loop par $B = 0$ dega. Ek loop, ek field, do answers: jaisa yeh law abhi hai, jab bhi kahin charge jama ho raha ho, yeh khud ko hi contradict karta hai.

3/3 $S_{2}$ ko ek badhta hua electric field cross karta hai. Uska flux us rate se badalta hai jiske liye $ε_{0} d Φ_{E} / d t = i$ .

Fig. 8.2Ek loop, do surfaces. Wire flat surface ko cross karti hai lekin balloon ko nahi, phir bhi dono ko loop ke around same magnetic field dena chahiye.NCERT Fig. 8.1 · p. 203

Ek vertical wire current i ko parallel-plate capacitor ki lower plate tak upar le jaati hai, capacitor perspective mein bana hai; lower plate par plus signs aur upper plate par minus signs hain. Lower plate ke neeche radius r ka ek blue circular loop wire ko gherta hai, aur arrows dikhate hain ki magnetic field B uske around ghoomta hai. Right mein ek panel batata hai ki Ampere's law kya deta hai. Step 1: loop par ek flat green disc S1 hai jise wire cheerti hai, aur panel par likha hai: through S1, current i, isliye B times 2 pi r barabar mu nought i. Step 2: disc ki jagah same rim wali ek purple balloon jaisi surface S2 aati hai, jo lower plate ke around upar uthti hai aur plates ke beech gap mein band hoti hai; koi wire use cross nahi karti, aur panel par likha hai: through S2, no current, B times 2 pi r barabar zero, saath mein ek question mark. Step 3: gap mein orange electric field lines dikhti hain jo positive se negative plate ki taraf upar point karti hain aur S2 ko cross karti hain, aur panel par likha hai: through S2, changing electric flux, epsilon nought times d Phi E by d t barabar i.

$S_{2}$ ko kuch na kuch cross karna chahiye jo current ka role nibhaye. Gap mein sirf plates ke beech ka electric field hai, aur jab tak capacitor charge hota hai, woh field badhta rehta hai. Chalo nikaalte hain ki $S_{2}$ se uska flux kitni tezi se badhta hai.

DerivationGap mein chhupa current

Maan lo har plate ka area $A$ hai, aur time $t$ par plates par charges $\pm Q$ hain. Plates ke beech field uniform hai, magnitude $E = Q / (ε_{0} A)$ , aur positive plate se negative plate ki taraf point karta hai. Edges ke paas ke chhote fringe field ko ignore karein to plates ke bahar field negligible hai. Field lines $S_{2}$ ke sirf us hisse ko cross karti hain jo gap mein hai, aur usse right angle par, isliye $S_{2}$ se electric flux hai

Φ_{E} = E A = \frac{Q}{ε_{0} A} A = \frac{Q}{ε_{0}}

(8.3)

Plates par charge thik usi rate se badhta hai jis rate se wire use deti hai, $d Q / d t = i$ . (8.3) ko time ke respect mein differentiate karne par $d Φ_{E} / d t = (1 / ε_{0}) d Q / d t = i / ε_{0}$ milta hai, yaani

ε_{0} \frac{d Φ_{E}}{d t} = i

(8.4)

$S_{2}$ se quantity $ε_{0} d Φ_{E} / d t$ ki units current ki hain, aur yeh $S_{1}$ se guzarne wale conduction current ke bilkul barabar hai. Agar hum ise Ampère's law mein current ki tarah ginein, to contradiction gayab ho jaata hai: dono surfaces se same total current $i$ guzarta hai.

Definition

Displacement current

Quantity $i_{d} = ε_{0} d Φ_{E} / d t$ , jahan $Φ_{E}$ kisi surface se electric flux hai. Koi charge nahi behta, phir bhi yeh bilkul utne hi conduction current ki tarah magnetic field banata hai.

ExampleJab capacitor $0.50 A$ se charge hota hai, to uski plates ke beech gap mein $0.50 A$ ka displacement current guzarta hai.

Jaana-pehchana current, jo chalte charges le jaate hain, ab conduction current $i_{c}$ kehlata hai. Maxwell ka generalisation yeh hai ki dono tarah ke currents magnetic field banate hain, aur Ampère's law mein current in dono ka sum hai:

i = i_{c} + i_{d} = i_{c} + ε_{0} \frac{d Φ_{E}}{d t}

(8.5)

LawAmpère–Maxwell law

Kisi bhi closed loop ke around $𝐁$ ka line integral $μ_{0}$ times us loop se bounded kisi bhi surface se guzarne wala total current (conduction plus displacement) hota hai.

Ampère–Maxwell law

\oint 𝐁 \cdot d 𝐥 = μ_{0} i_{c} + μ_{0} ε_{0} \frac{d Φ_{E}}{d t}

(8.6)

(8.6) ko ek baar phir Fig. 8.2 ke loop par lagao. Flat surface $S_{1}$ plates ke bahar hai, jahan electric field nahi hai, isliye use sirf conduction current cross karta hai. Balloon $S_{2}$ ko koi wire cross nahi karti, isliye use sirf displacement current cross karta hai. Dono $i$ ke barabar hain, aur dono ab $B (2 π r) = μ_{0} i$ dete hain. Field ab is par depend nahi karta ki hum kaunsi surface chunte hain, aur nature ke law ko yahi guarantee karna chahiye. Law ke is form ko Ampère–Maxwell law kehte hain.

Compare

Do tarah ke current

Conduction current $i_{c}$

Charges sach mein chalte hain
Wires, electrolytes aur ionised gases mein milta hai
Bilkul steady ho sakta hai
Jis conductor mein behta hai use garam karta hai ( $I^{2} R$ )
Apne around magnetic field banata hai

Displacement current $i_{d}$

Koi charge nahi chalta; surface se electric flux badalta hai
Jahan bhi electric field badalta hai wahan milta hai: capacitor gaps, insulators, empty space
Electric field steady ho to zero
Empty space mein koi heating nahi karta
Bilkul usi tarah magnetic field banata hai

Real materials kabhi perfect conductor ya perfect insulator nahi hote, isliye unmein dono tarah ke current aksar saath-saath behte hain. Lekin doosre column mein is chapter ki chaabi chhupi hai. Sun aur Earth ke beech ke space ko socho, jismein na wires hain aur lagbhag koi charges bhi nahi. Agar wahan electric field badalta hai, to Ampère–Maxwell law kehta hai ki ek magnetic field us change ke around ghoomega, bilkul waise hi jaise woh $ε_{0} d Φ_{E} / d t$ current wali wire ke around ghoomta. Isliye magnetic fields un regions mein bhi ban sakte hain jahan bilkul conduction current nahi hai, aur isi wajah se electromagnetic waves exist kar paati hain.

Kya displacement current real hai? Uska magnetic field to real hai. Charge ho rahi circular plates ke beech ek magnetic field capacitor ke axis ke around ghoomta hai, jaisa Fig. 8.3 mein hai. Axis se plate radius se zyada kisi bhi distance par, gap ke plane mein field ki value utni hi hoti hai jitni wire se usi distance par. Careful measurements isko confirm karte hain. Jab charging rukti hai, electric field badalna band ho jaata hai aur gap ka magnetic field gayab ho jaata hai; jab capacitor discharge hota hai, to field ulti direction mein wapas aa jaata hai.

1/3Jab capacitor charge hota hai, $𝐄$ badhta hai aur ek magnetic field gap ke around ghoomta hai, upar se dekhne par anticlockwise.

Fig. 8.3Gap ke around magnetic field sirf tab ghoomta hai jab plates ke beech electric field badal raha ho, aur uski direction is par depend karti hai ki field badh raha hai ya ghat raha hai.NCERT Fig. 8.2 · p. 204

Left: parallel-plate capacitor ka side view, upar negative plate aur neeche positive plate, gap ke across upar point karte orange electric field arrows, aur field ki strength dikhata ek bar gauge. Right: upar se dekha gaya gap, jismein electric field orange dots (page se bahar point karte) se aur axis ke around magnetic field blue circles se dikhaya gaya hai. Step 1: current wires mein upar behta hai, gauge par rising likha hai, aur blue circles par anticlockwise chalte arrows hain. Step 2: koi current nahi behta, gauge bhara hua hai aur us par steady likha hai, aur blue circles gayab ho gaye hain. Step 3: current wires mein neeche behta hai, gauge par falling likha hai, aur blue circles clockwise arrows ke saath wapas aa jaate hain.

DerivationCircular plates ke beech magnetic field

Maan lo plates radius $R$ ki discs hain, jo current $i$ se charge ho rahi hain. Gap mein radius $r$ ka ek circular loop lo, axis par centred aur plates ke parallel. Symmetry se $B$ loop ka tangent hai aur poore loop par same size ka hai. Loop par phaili flat disc ko sirf displacement current cross karta hai.

Agar $r \geq R$ hai, to disc plates ke beech ka poora electric flux pakad leti hai, isliye enclosed displacement current poora $i$ hai aur

B = \frac{μ_{0} i}{2 π r} (r \geq R)

Agar $r < R$ hai, to plates ke beech field uniform hone se disc flux ka sirf $π r^{2} / π R^{2}$ hissa pakadti hai, aur displacement current ka bhi:

B (2 π r) = μ_{0} i \frac{r^{2}}{R^{2}} ⟹ B = \frac{μ_{0} i r}{2 π R^{2}} (r < R)

Field axis par zero se shuru hokar $r$ ke proportion mein badhta hai aur plates ke rim par apni sabse badi value $μ_{0} i / 2 π R$ tak pahunchta hai. Rim ke aage yeh $1 / r$ ki tarah ghatta hai, bilkul wire ke around field ki tarah (Fig. 8.4).

3/3Field axis par zero hai, plates ke rim par sabse bada hai, aur bahar ghatta jaata hai.

Fig. 8.4Plates ke beech

B

rim tak linearly badhta hai aur phir

1 / r

ki tarah ghatta hai, bilkul wire ke around field ki tarah.

Magnetic field B (upar) ka axis se distance r (across) ke against graph, plate radius R par ek dashed vertical line ke saath. Right mein plate ka ek chhota top view dikhata hai ki loop displacement current ka kaunsa hissa gherta hai. Step 1: curve ka sirf bahari hissa bana hai, jo R ke aage mu nought i over 2 pi r ki tarah ghatta hai; inset mein plate se bada loop poori shaded plate ko gherta hai, isliye enclosed displacement current i ke barabar hai. Step 2: origin se R tak seedhi line banti hai, jis par mu nought i r over 2 pi R squared likha hai; inset mein ek chhota loop sirf andar ki shaded disc gherta hai, yaani r squared over R squared hissa. Step 3: dono hisse saath mein bane hain aur r barabar R par peak par ek dot hai, jis par B max barabar mu nought i over 2 pi R likha hai.

Example

Charging capacitor ke andar field

$5.0 c m$ radius ki circular plates wala ek capacitor $1.2 A$ ke steady current se charge ho raha hai. Gap mein axis se (a) $2.0 c m$ aur (b) $10 c m$ door magnetic field nikaalo. (c) Plates ke beech field kahan sabse strong hai, aur wahan kitna strong hai? $μ_{0} = 4 π \times 10^{- 7} T m / A$ lo.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

InteractiveCharging capacitor ke around field

5 cm radius ki circular plates wala ek interactive capacitor, jo ek vertical wire se charge hota hai. Tum chunte ho ki circular loop wire ke around ho ya plates ke beech gap mein, aur us par flat disc phaili ho ya gap se guzarta bag. Sliders loop radius ko 0.5 se 12 cm tak aur current ko minus 2 se plus 2 amperes tak set karte hain. Readouts chuni hui surface se conduction current, displacement current aur total current dikhate hain, aur loop par magnetic field uski direction ke saath. Ek graph gap mein aur wire ke around field ko loop radius ke against plot karta hai, current setting ke liye ek dot ke saath.

Fig. 8.5Loop ko wire ke around ya gap mein le jao, uska radius aur current badlo, aur dekho ki woh kitna conduction aur displacement current gherta hai.

Fig. 8.1 ko phir dekho. Maxwell se pehle dono fields ke beech sirf ek arrow tha: changing magnetic field electric field banata hai (Faraday's law). Ampère–Maxwell law doosri direction ka arrow deta hai, isliye ab har field doosre ka source ban sakta hai.Yeh symmetry perfect nahi hai. Electric field lines charges par shuru aur khatam hoti hain, lekin koi akela magnetic pole (monopole) aaj tak nahi mila, isliye magnetic field lines hamesha khud par hi band hoti hain. Dono fields ke Gauss's laws ke saath milkar yeh do laws Table 8.1 ka poora set banate hain.

Table 8.1Vacuum mein Maxwell's equations, integral form mein

Law	Equation	Yeh kya kehta hai
$𝐄$ ke liye Gauss's law	$\oint 𝐄 \cdot d 𝐀 = Q / ε_{0}$	Electric field lines charges par shuru aur khatam hoti hain; bahar ki taraf flux enclosed charge ko naapta hai.
$𝐁$ ke liye Gauss's law	$\oint 𝐁 \cdot d 𝐀 = 0$	Magnetic charges nahi hote; magnetic field lines closed loops banati hain.
Faraday's law	$\oint 𝐄 \cdot d 𝐥 = - \frac{d Φ_{B}}{d t}$	Changing magnetic flux ek electric field banata hai jo uske around ghoomta hai.
Ampère–Maxwell law	$\oint 𝐁 \cdot d 𝐥 = μ_{0} i_{c} + μ_{0} ε_{0} \frac{d Φ_{E}}{d t}$	Currents aur changing electric flux ek magnetic field banate hain jo unke around ghoomta hai.

Isme Lorentz force $𝐅 = q (𝐄 + 𝐯 \times 𝐁)$ jodo, jo batata hai ki charges fields par kaise respond karte hain, aur poora classical electromagnetism paanch lines mein aa jaata hai. Agla section dikhata hai ki jab bilkul koi charges ya currents na hon, tab beech ke do equations kya karte hain.

Quick check

4 mein se 1

Ek capacitor charge ho raha hai. Uski plates ke beech ke region ke baare mein kaunsa statement sahi hai?

Gap ke across conduction current behta haiGap ko kisi bhi tarah ka current cross nahi karta, isliye wahan koi magnetic field nahi haiDisplacement current behta hai, lekin woh hamesha leads ke current se chhota hota haiLeads ke current ke barabar displacement current gap ko cross karta hai

Answer dekho

Answer (D) Leads ke current ke barabar displacement current gap ko cross karta hai

Gap ko koi charge cross nahi karta, isliye wahan conduction current nahi hai. Lekin gap mein electric flux thik us rate se badalta hai jo

ε_{0} d Φ_{E} / d t = i

ke liye chahiye, isliye displacement current leads ke current ke barabar hai aur gap mein magnetic field banata hai.

Maxwell's equations

Maxwell ke har equation ko us baat se match karo jo woh humein batata hai.

Left mein koi item tap karo, phir right mein uska match.

Answer dekho

Answer

E ke liye Gauss's law : Charges electric field lines ke sources hain
B ke liye Gauss's law : Magnetic charges nahi hote
Faraday's law : Changing magnetic flux electric field banata hai
Ampère–Maxwell law : Currents aur changing electric flux magnetic field banate hain

Har law ek tarah ka source batata hai: E ke liye charges, B ke liye kuch nahi (monopoles nahi hote), ghoomte E ke liye changing B, aur ghoomte B ke liye currents plus changing E.

8.3 Electromagnetic waves

Changing electric field magnetic field banata hai, aur changing magnetic field electric field banata hai. In dono baaton ko saath rakho to ek kamaal ki possibility khulti hai: ek aisa disturbance jismein har field doosre ko banata rehta hai, aur bina kisi carrier ke space mein aage badhta jaata hai. Yeh section poochta hai ki aisa disturbance kaun banata hai aur woh dikhta kaisa hai.

8.3.1 Electromagnetic waves ke sources

Transmitter mast asal mein karta kya hai? Uske antenna (ऐन्टेना) ke andar ek oscillator electrons ko metal mein ek second mein kai million baar upar-neeche chalata hai. Jaise-jaise woh upar-neeche bhaagte hain, antenna ke paas electric field badalta rehta hai. Changing electric field ek displacement current hai, isliye uske around ek changing magnetic field ghoomta hai. Faraday's law se woh changing magnetic field thoda aur bahar ek changing electric field banata hai, jo phir aur bahar ek magnetic field banata hai. Har field doosre ko chalata rehta hai, aur pattern light ki speed se bahar phailta hai (Fig. 8.6). Beech se feed ki gayi aisi do rods ek oscillating electric dipole banati hain, jo electromagnetic waves ka sabse simple source hai.

4/4Har cycle ek wavelength jodti hai, isliye $λ = c T = c / ν$ aur wave ki frequency source wali $ν$ hai.

Fig. 8.6Oscillating charge har cycle mein field pattern ki ek aur wavelength bhejta hai, isliye wave ki frequency uske source wali hoti hai.

Left mein do metal rods ka bana ek vertical antenna hai jise beech se frequency nu wala oscillator feed karta hai. Antenna se right ki taraf ek dashed horizontal line jaati hai. Step 1: oscillator off hai, antenna idle hai aur koi field pattern nahi hai. Step 2: rods ke paas double-headed red arrows charge ko upar-neeche bhaagta dikhate hain; orange electric field arrows ki ek wavelength, baari-baari se upar aur neeche point karte, antenna se ek dashed wave front tak phaili hai jo speed c se door jaata hai. Step 3: front do guna door chala gaya hai aur pattern ki do wavelengths hain. Step 4: teen wavelengths hain, aur doosri ke neeche ek bracket par lambda likha hai.

Table 8.2Kaunse chalte charges radiate karte hain?

Charge kaise chalta hai	Usse bane fields	Kya yeh radiate karta hai?
Ruka hua	static electric field	Nahi
Constant velocity se (steady current)	electric aur steady magnetic fields jo uske saath chalte hain	Nahi
Accelerating: speed badhna, ghatna, mudna ya oscillate karna	changing fields jo alag hokar bahar phailte hain	Haan

Table 8.2 ka rule Maxwell's equations se aata hai: sirf accelerated charges radiate karte hain. Acceleration mein direction ka change bhi shaamil hai, isliye constant speed se circle mein ghoomta charge bhi radiate karta hai.

Wave jo bhi energy le jaati hai, woh source ko deni padti hai. Isiliye transmitter apni supply se power leta rehta hai, bhale hi uske signal pakadne wale radios se koi wire na judi ho. Figure yeh bhi dikhata hai ki wave ki frequency source ke barabar kyun hoti hai: electrons ka har upar-neeche cycle thik ek aur wavelength launch karta hai.

Fig. 8.6 ki har wave ki frequency un charges wali hoti hai jo use launch karte hain. Antenna se green light ( $530 n m$ ) banane ke liye uske electrons ko ek second mein $5.7 \times 10^{14}$ baar aage-peeche jhoolna padega, aur har jhoola do femtoseconds se kam mein poora karna hoga. Koi circuit iske kareeb bhi nahi pahunchta: aaj ke sabse fast transistors lagbhag $10^{12} H z$ tak jaate hain, aur 1880s ke spark circuits kuch sau megahertz tak. Light oscillating charges se hi banti hai, lekin atoms ke andar, hamari banayi wires mein nahi. Isliye Maxwell ke claim ka test ulti taraf se karna pada. Circuit se kahin slow waves banao, phir dikhao ki woh light ki speed se travel karti hain aur baaki har tarah se light jaisa behave karti hain.

Heinrich Hertz ne 1887 mein bilkul yahi kiya (Fig. 8.7). Ek induction coil ne do metal rods ko, jinke beech chhota air gap tha, tab tak charge kiya jab tak spark nahi koodi. Jab tak spark rahi, charge rods ke beech bahut high frequency par aage-peeche bhaagta raha, aur rods ne radiate kiya. Kuch metres door, wire ke ek simple loop mein, jismein apna chhota sa gap tha, halki sparks dikhi: waves kamra paar kar chuki thi. Unhe metal sheet se reflect karke Hertz ne standing waves banayi, unke nodes ki spacing naap kar wavelength nikaali, aur use apne oscillator ki frequency se joda. Speed light ki speed ke kareeb aayi. Unhone yeh bhi dikhaya ki unki waves light ki tarah hi reflect, refract aur polarise ho sakti hain.

3/4Kuch metres door waves ring mein current chalati hain aur uske gap mein chhoti si spark koodti hai.

Fig. 8.7Maxwell ke prediction ka Hertz wala test: sparks waves banati hain, waves kamre ke us paar spark banati hain, aur standing waves unki wavelength batati hain.NCERT p. 206

Left mein ek transmitter: ek line mein do metal rods, har ek ke end par ek bada metal ball, aur unke andar wale ends ke beech chhota gap; neeche ek induction coil gap ke across judi hai. Right mein ek receiver: wire ki ek ring jiske upar chhota sa gap hai. Step 1: coil rods ko charge karti hai, left ball positive aur right ball negative, aur kuch aur nahi hota. Step 2: transmitter gap mein spark koodti hai aur dashed orange wave fronts right ki taraf phailte hain, abhi ring tak nahi pahunche. Step 3: wave fronts ring tak pahunchte hain aur uske gap mein chhoti si spark dikhti hai. Step 4: bilkul right mein ek metal sheet khadi hai; wave fronts ki jagah humps ki ek line aati hai jo transmitter aur sheet ke beech standing wave ki strength dikhati hai, sheet par aur aadhi wavelength ki doori wale points par zero, ring ek hump ke upar rakhi hai aur do zeros ke beech ek bracket par lambda over 2 likha hai.

Compare

Hertz ke baad: do raaste

Chhoti waves: J. C. Bose, Kolkata

5–25 mm lambi waves banayi (lagbhag 12–60 GHz), jo aaj ki microwave range mein hain
Bench par dikhaya ki woh light ki tarah reflect, refract aur polarise hoti hain
Horn antenna aur galena crystal detector invent kiya

Lambi range: G. Marconi, Italy aur England

Door tak pahunchne ke liye lambi waves aur oonche, earthed antennas chune
1901 mein Cornwall se Newfoundland tak Atlantic paar kiya
Radio ko ships ke liye ek service banaya, aur 1909 ka Nobel Prize in Physics share kiya

Ghar par try karo

Sparks sunne wala radio

Tumhe chahiye

ek AM (medium-wave) radio
ek 9 V battery
wire ka chhota tukda ya steel ki chaabi
spark wala kitchen gas lighter (optional)

Pehle guess karo

Har baar jab tum radio ke paas wire ko battery terminals ke across chhuaoge, tumhe kya sunai dega?

Kuch nahi: battery steady current deti haiJab tak wire chhooti rahe, ek steady humHar baar circuit judne ya tootne par ek click ya crackle

AM (medium-wave) radio ko do stations ke beech ek shaant jagah par tune karo aur volume badhao.
9 V battery ko radio se lagbhag $20 c m$ door pakdo. Wire ke chhote tukde ko uske dono terminals ke across ek pal ke liye chhuao, baar-baar.
Thoda aur door se dohrao, aur phir radio ke paas kitchen gas lighter (spark wala) click karke dekho.

8.3.2 Electromagnetic waves ka nature

Source se door, wave ka chhota sa patch ek plane wave jaisa dikhta hai: travel ki direction ke perpendicular kisi bhi plane par fields har jagah same hote hain. Tum samajh sakte ho ki ismein fields ek doosre ke perpendicular kyun hone chahiye. Faraday's law electric field ko changing magnetic field ke around ghumata hai, aur Ampère–Maxwell law magnetic field ko changing electric field ke around ghumata hai. Jo field kisi doosre ke around ghoomta hai, woh usse right angle par hota hai. Maxwell's equations yeh bhi dikhate hain ki kisi bhi field ka travel ki direction mein component nahi hota. To $𝐄$ , $𝐁$ aur travel ki direction aapas mein perpendicular hain, aur electromagnetic wave ek transverse wave hai.

$+ x$ axis ke along chalti ek wave lo jiska electric field $y$ ke along hai. Fig. 8.8 ek snapshot dikhata hai. Tab magnetic field $z$ ke along point karta hai, aur har point par dono fields saath-saath badhte aur ghatte hain:

E_{y} = E_{0} \sin (k x - ω t)

(8.7(a))

B_{z} = B_{0} \sin (k x - ω t)

(8.7(b))

2/4 $𝐁$ , $\pm z$ ke along point karta hai (page se bahar ya andar). Jahan $𝐄$ sabse bada hai wahan yeh sabse bada hai, aur jahan $𝐄$ zero hai wahan zero: fields same phase mein hain.

Fig. 8.8Electric field, magnetic field aur travel ki direction teen aapas mein perpendicular directions mein point karte hain, aur dono fields saath-saath badhte aur ghatte hain.NCERT Fig. 8.3 · p. 206

Figure ke across ek horizontal line hai, aur top right par ek arrow dikhata hai ki wave right ki taraf chalti hai. Line par khade orange arrows barabar doori wale points par electric field dikhate hain: woh upar aur neeche point karte hain aur unki lengths sine curve follow karti hain, aur ek crest arrow red mein mota bana hai. Step 1: sirf electric field arrows dikhte hain. Step 2: neeche ek doosri row unhi points par magnetic field ko blue circles se dikhati hai, jahan E upar hai wahan page se bahar ke liye circle mein dot aur jahan E neeche hai wahan page ke andar ke liye circle mein cross, aur yeh wahan sabse bade hain jahan E arrows sabse lambe hain. Step 3: chauthai period baad poora pattern right ki taraf chauthai wavelength khisak gaya hai; ek dashed line dikhati hai ki red crest pehle kahan thi aur lambda over 4 likha bracket batata hai ki woh kitna chali. Step 4: rows lagbhag poori tarah halki pad jaati hain aur teen arrows ka ek bada set dikhta hai: E upar point karta hai, B page se bahar point karta hai (viewer ki taraf tircha bana hai aur us par out of page likha hai) aur travel ki direction right point karti hai.

Yahan $E_{0}$ aur $B_{0}$ amplitudes hain, $ω = 2 π ν$ angular frequency hai, aur $k$ wave number hai, jise propagation constant bhi kehte hain. Travel ki direction mein point karne wala $k$ size ka vector wave vector $𝐤$ hai. Travel ki direction hamesha $𝐄 \times 𝐁$ ki direction hoti hai; yahan $\hat{𝐣} \times \hat{𝐤} = \hat{𝐢}$ , jaisa chahiye, $+ x$ ke along.

DerivationWavelength, speed aur frequency

Kisi bhi fixed instant par pattern (8.7) tab repeat hota hai jab $k x$ , $2 π$ se badhta hai. Yeh distance wavelength hai, isliye

k = \frac{2 π}{λ}

(8.8)

Ab ek crest ko follow karo. Crest fixed phase wala point hai, $k x - ω t = constant$ . Time ke respect mein differentiate karne par $k d x / d t - ω = 0$ milta hai, isliye crest $d x / d t = ω / k$ se chalti hai. Jab (8.7) ko Maxwell's equations mein daalte hain, to woh tabhi satisfy hote hain jab is speed ki ek khaas value ho, jo sirf $μ_{0}$ aur $ε_{0}$ se fix hoti hai:

ω = c k, c = \frac{1}{\sqrt{μ_{0} ε_{0}}}

(8.9(a))

$ω = 2 π ν$ aur $k = 2 π / λ$ likhne par $ω = c k$ ban jaata hai $2 π ν = 2 π c / λ$ , yaani jaana-pehchana wave relation

c = ν λ

(8.9(b))

$μ_{0} = 4 π \times 10^{- 7} T m / A$ aur $ε_{0} = 8.854 \times 10^{- 12} C^{2} N^{- 1} m^{- 2}$ ke saath (8.9a) se $c = 2.998 \times 10^{8} m / s$ milta hai.

3/3Ek fixed point par $E_{y}$ time ke saath period $T = 1 / ν$ se oscillate karta hai.

Fig. 8.9Snapshot wavelength dikhata hai; ek point ko dekhte rehne se period dikhta hai. Pattern ek period mein ek wavelength chalta hai, isliye

c = λ / T = ν λ

Upar: ek instant par E y ka x ke against graph, amplitude E nought wala sine curve, jismein paas ki crests ke beech ek bracket ek wavelength lambda mark karta hai. Step 1: t barabar 0 ke liye sirf yeh orange curve dikhta hai. Step 2: chauthai period baad ke liye ek dashed red curve judta hai; uski shape same hai bas right ki taraf khiski hui, aur paas ki crests ke beech ek arrow par lambda over 4 likha hai. Step 3: neeche ek doosra graph aata hai jo single point x barabar 0 par E y ko time t ke against dikhata hai: ek green sine curve jiski paas ki crests ek period T ki doori par hain, jise bracket mark karta hai.

Maxwell's equations dono amplitudes ko bhi jodte hain:

B_{0} = \frac{E_{0}}{c}

(8.10)

Kyunki fields same phase mein hain, $E = c B$ har point aur har instant par sach hai, sirf peaks par nahi. Factor $c$ ki wajah se SI units mein magnetic field bahut chhota dikhta hai: $E_{0} = 3.0 V / m$ wale strong radio signal ka $B_{0} = 1.0 \times 10^{- 8} T$ hai, jo Earth ke field ka lagbhag paanch-hazaarvaan hissa hai. Phir bhi, jaisa hum dekhenge, dono fields wave ki energy ka barabar hissa le jaate hain. Fig. 8.10 use karke wave ko chalte dekho, uski frequency aur medium badlo, aur ek point par dono fields padho.

InteractiveChalti hui electromagnetic wave

x ke along chalti plane electromagnetic wave ka animated three-dimensional view, jismein y ke along orange electric field arrows aur z ke along blue magnetic field arrows hain; ise drag karke ya 3-D, side ya top view chun kar ghuma sakte ho. Controls wave ko pause karte hain, ek step aage badhate hain, travel ki direction ulti karte hain, har field ko dikhate ya chhupate hain, frequency 100 se 500 megahertz aur electric field amplitude 1 se 60 volts per metre tak set karte hain, aur wave ko vacuum mein ya relative permittivity 2.25 ya 4 wale materials mein daalte hain. Readouts wavelength, speed, period, magnetic amplitude, wave number aur angular frequency batate hain, aur ek probe ek point par dono fields ko unki values ke time ke saath scroll hote graph ke saath dikhata hai.

Fig. 8.10Slow motion mein ek plane wave. Probe ek point par

E_{y}

aur

B_{z}

dikhata hai; uske neeche ka graph unhe time ke saath trace karta hai.

Example 8.1NCERT Example 8.1 · p. 208

Known electric field ka magnetic partner

$150 M H z$ frequency ki ek radio wave hawa mein seedhe north ki taraf chalti hai (uski speed $c$ lo). Ek khaas point aur instant par uska electric field $4.8 V / m$ hai, jo vertically upar point karta hai. $x$ ko east ki taraf, $y$ ko north ki taraf aur $z$ ko vertically upar lo. Us point aur instant par (a) wavelength aur (b) magnetic field, magnitude aur direction dono, nikaalo.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Example 8.2NCERT Example 8.2 · p. 208

Wave equation padhna

Vacuum mein ek plane electromagnetic wave ka electric field $E_{y} = (45 V / m) \sin [(1.5 \times 10^{2} m^{- 1}) x - (4.5 \times 10^{10} s^{- 1}) t]$ hai. (a) Uski wavelength aur frequency nikaalo, aur spectrum ka region batao. (b) Yeh kis direction mein chalti hai? (c) Uske magnetic field ka expression likho.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Quick check

3 mein se 1

Vacuum mein ek electromagnetic wave ka electric field amplitude

21 V / m

hai. Uska magnetic field amplitude kitna hai, nanotesla mein?

Answer dekho

Answer 70 nT

B_{0} = E_{0} / c = 21 / (3.0 \times 10^{8}) = 7.0 \times 10^{- 8} T = 70 n T

Sound ko hawa chahiye aur string par wave ko string, lekin electromagnetic wave ko kuch nahi chahiye. Uske fields self-sustaining hain: har ek doosre ke changes se chalta rehta hai. Isiliye Sun ki light, aur arabon light years door galaxies ki light bhi, lagbhag khaali space paar karke hum tak pahunchti hai.

Glass mein light slow ho jaati hai, lagbhag $2.0 \times 10^{8} m / s$ tak. Wajah yeh hai ki glass ke atoms ke charges wave ke electric field se aage-peeche dhakele jaate hain, aur unke apne chhote fields usmein jud jaate hain. Maxwell's equations mein iska dhyaan $ε_{0}$ ki jagah material ki permittivity $ε = ε_{r} ε_{0}$ , aur $μ_{0}$ ki jagah uski permeability $μ = μ_{r} μ_{0}$ rakh kar rakha jaata hai. Tab wave speed ban jaati hai

Material mein speed

v = \frac{1}{\sqrt{μ ε}} = \frac{c}{\sqrt{μ_{r} ε_{r}}}

(8.11)

Zyadatar transparent materials non-magnetic ( $μ_{r} \approx 1$ ) hote hain aur unka $ε_{r} > 1$ hota hai, isliye unmein waves vacuum se slow chalti hain. $ε_{r}$ frequency par depend karta hai. Paani ke liye slowly varying fields mein yeh lagbhag 80 hai lekin light ki frequencies par sirf lagbhag 1.8, isliye paani ka refractive index $\sqrt{80}$ nahi balki 1.33 hai. Boundary par frequency nahi badal sakti, kyunki jo bhi crest aati hai use aage jaana hi hai, isliye wavelength usi proportion mein chhoti hoti hai jismein speed (Fig. 8.11). Ratio $c / v$ material ka refractive index hai, jahan se Chapter 9 shuru hota hai.

2/3 $ε_{r} = 2.25$ wale non-magnetic material mein $v = c / \sqrt{2.25} = c / 1.5$ , isliye wavelength ghat kar $λ_{0} / 1.5$ ho jaati hai.

Fig. 8.11Material mein jaane se frequency nahi badalti, isliye slow speed ka matlab chhoti wavelength hai.

Ek orange sine wave dashed line ke along left se right chalti hai. Left hisse ke neeche ek bracket vacuum mein ek wavelength, lambda nought, mark karta hai. Step 1: poori width vacuum hai aur wave ki wavelength har jagah same hai. Step 2: right aadha hissa relative permittivity 2.25 wale material ka halka blue slab ban jaata hai; uske andar wave apni vacuum wavelength ke do-tihai tak sikud jaati hai, jise doosra bracket mark karta hai, aur speed par c over 1.5 likha hai. Step 3: slab ki jagah relative permittivity 4 wala purple material aata hai; andar wavelength ab vacuum value ki aadhi hai aur speed c over 2 hai. Dono material steps mein wave boundary par smoothly judti hai aur ek label batata hai ki frequency nahi badli.

Example

Cable mein signals

$500 M H z$ television signal le jaane wali coaxial cable ke andar ki jagah polythene se bhari hai, jiske liye $ε_{r} = 2.25$ aur $μ_{r} = 1$ . Nikaalo (a) cable mein signal ki speed, (b) hawa mein aur cable mein uski wavelength, aur (c) $30 m$ cable se aane wala delay.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Radio waves, light, X-rays aur gamma rays ke experiments mein vacuum mein unki speeds ke beech koi bhi fark nahi milta. Physicists ab $c$ par itna bharosa karte hain ki 1983 se ise naapa nahi jaata balki exactly $299 792 458 m / s$ define kiya gaya hai. Ab metre woh distance hai jo light vacuum mein second ke $1 / 299 792 458$ hisse mein tay karti hai.

Electromagnetic waves energy le jaati hain. Sunlight zameen ko garam karti hai aur photosynthesis ko power deti hai, aur broadcast signal har us antenna tak thodi si power pahunchata hai jahan tak woh jaata hai. Chapters 2 aur 6 se, electric field per unit volume $\frac{1}{2} ε_{0} E^{2}$ energy store karta hai aur magnetic field $B^{2} / 2 μ_{0}$ . Wave ki energy uske do fields mein kaise bantti hai?

DerivationEnergy ke barabar hisse

Wave ke kisi bhi point par $B = E / c$ , aur $c^{2} = 1 / μ_{0} ε_{0}$ . Isliye magnetic energy density hai

u_{B} = \frac{B^{2}}{2 μ_{0}} = \frac{E^{2}}{2 μ_{0} c^{2}} = \frac{μ_{0} ε_{0} E^{2}}{2 μ_{0}} = \frac{1}{2} ε_{0} E^{2} = u_{E}

Dono fields har point aur har instant par barabar energy rakhte hain, isliye total energy density $u = ε_{0} E^{2}$ hai. Kyunki ek cycle mein $E^{2} = E_{0}^{2} \sin^{2} (k x - ω t)$ ka average $\frac{1}{2} E_{0}^{2}$ hota hai, wave ki average energy density hai

Average energy density

\overset{ˉ}{u} = {\overset{ˉ}{u}}_{E} + {\overset{ˉ}{u}}_{B} = \frac{1}{4} ε_{0} E_{0}^{2} + \frac{1}{4} ε_{0} E_{0}^{2} = \frac{1}{2} ε_{0} E_{0}^{2}

Example

Transmitter ke paas energy

Broadcasting tower ke paas radio wave ke electric field ka amplitude $6.0 V / m$ hai. Nikaalo (a) magnetic field amplitude, (b) uske electric aur magnetic fields ki average energy densities, aur (c) total average energy density. ( $ε_{0} = 8.85 \times 10^{- 12} C^{2} N^{- 1} m^{- 2}$ , $μ_{0} = 4 π \times 10^{- 7} T m / A$ )

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Ghar par try karo

Apne kitchen mein light ki speed naapo

Tumhe chahiye

ek microwave oven (kisi bade ki permission ke saath)
chocolate ki ek badi flat bar, ya plate par grated cheese
ek ruler

Pehle guess karo

Waves oven ki metal walls ke beech uchhalti hain aur standing waves banati hain. Chocolate sabse pehle kahan pighlegi?

Lagbhag aadhi wavelength ki doori wale spots parPoori bar par ek jaisiSirf centre mein, jahan turntable ka axle tha

Microwave oven se turntable nikaalo aur uski jagah ek ulti plate rakho, taaki khana ghoom na sake.
Us par chocolate ki ek badi flat bar (ya grated cheese se barabar dhaki plate) rakho.
Low setting par 15–25 s garam karo, jab tak kuch naram ya pighle spots na dikhein, phir bahar nikaalo.
Paas-paas ke pighle spots ke beech distance $d$ naapo, oven ke rating label par frequency $ν$ padho (aksar $2450 M H z$ ), aur $c = 2 d ν$ calculate karo.

Table 8.3Tumhara measurement

	Value
Spot spacing $d$ (m)
Frequency $ν$ (Hz)
$c = 2 d ν$ (m/s)

Tumhari entries apne aap save hoti hain.

Quick check

4 mein se 1

Ek non-magnetic plastic ka

ε_{r} = 4.0

hai. Usmein electromagnetic waves kis speed se chalti hain, metres per second mein?

m/s

Answer dekho

Answer 150000000 m/s

v = c / \sqrt{ε_{r}} = 3.0 \times 10^{8} / 2 = 1.5 \times 10^{8} m / s

8.4 Electromagnetic spectrum

Electromagnetic waves ke liye saat naam roz use hote hain: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays aur gamma rays. Yeh lagbhag ek sadi mein ek-ek karke discover hue, aksar aise logon ne jinhe pata hi nahi tha ki woh sab ek hi cheez dekh rahe hain. Yeh ek hi phenomenon hain, jo sirf frequency, ya isi baat ko doosre tareeke se kahein to wavelength, mein alag hain. Order mein lagane par yeh electromagnetic spectrum (वैद्युतचुंबकीय स्पेक्ट्रम) banate hain.

Timeline

Spectrum ko bharna

1800
Herschel: infrared
Prism ke spectrum ke red end se aage rakha thermometer visible colours mein rakhe thermometer se zyada garam hua.
1801
Ritter: ultraviolet
Silver chloride violet end ke thik aage, jahan kuch dikhta nahi tha, sabse tezi se kaala pada.
1865
Maxwell ka prediction
Electromagnetic waves honi chahiye aur light ki speed se chalni chahiye; light khud inmein se ek hai.
1887
Hertz: radio waves
Spark gap se nikli waves laboratory ke us paar detect hui, aur unki speed naapi gayi.
1895
Röntgen: X-rays
Discharge tube se nikli rays card aur flesh ke aar-paar gayi aur photographic plate par haath ki haddiyan dikha di.
1895
Bose: millimetre waves
Kolkata ke ek public demonstration mein unki short-wavelength waves ne doosre kamre mein ghanti bajayi aur chutki bhar gunpowder jalaya.
1900
Villard: gamma rays
Radium ne bahut penetrating radiation nikaali jise magnet deflect nahi kar saka.
1901
Marconi: Atlantic ke paar
England ke Cornwall se bheja radio signal samundar ke us paar Newfoundland mein receive hua.

Fig. 8.12 spectrum ko logarithmic scale par dikhata hai, jahan har step wavelength mein das guna ka factor hai; visible light do guna se bhi kam chaudi ek patli si patti hai. Naam regions ke labels hain, sharp boundaries nahi, aur paas ke regions overlap karte hain. $0.01 n m$ wavelength wale photon ko X-ray kehte hain agar woh X-ray tube se aaya ho, aur gamma ray agar nucleus se aaya ho, phir bhi wave khud same hai. Neeche hum sabse lambi wavelengths se sabse chhoti tak regions se guzarte hain. Fig. 8.13 se tum khud inhe explore kar sakte ho.

2/4Left se right frequency badhti hai aur wavelength ghatti hai, kyunki $ν = c / λ$ .

Fig. 8.12Scale par har step das guna ka factor hai. Regions ek doosre mein mil jaate hain; visible light ek bahut patli slice hai.NCERT Fig. 8.4 · p. 209

Ek lambi horizontal bar coloured regions mein bati hai, left mein radio waves se shuru hokar microwaves, infrared, ek patli yellow visible slice, ultraviolet, X-rays aur right mein gamma rays tak; X-rays aur gamma rays overlap karte hain. Bar ke neeche ek wavelength scale par 1 km, 1 m, 1 mm, 1 micrometre, 1 nm aur 1 pm mark hain, har step das guna ka factor. Step 1: region names ke saath bar. Step 2: bar ke upar ek frequency scale aata hai, left mein 10 to the 6 hertz se right mein 10 to the 21 hertz tak. Step 3: scale ke neeche cheezon ki ek row upar ki wavelengths jitne size dikhati hai: ek ghar, ek coin, ek living cell, ek atom aur ek atomic nucleus. Step 4: cheezon ki jagah visible slice ki ek badi patti aati hai, jo left mein 700 nm par red se orange, yellow, green aur blue hokar right mein 400 nm par violet tak jaati hai.

InteractiveSpectrum explorer

Ek interactive spectrum bar jo logarithmic scale par left mein 10 kilometres se right mein 10 to the minus 14 metres tak chalti hai, upar frequency marks aur neeche wavelength marks ke saath. Bar par marker drag karne, slider chalane, FM station, microwave oven, TV remote, germicidal lamp ya cobalt-60 jaisa koi example tap karne, ya hertz, metres ya electronvolts mein value type karne par region ka naam, wavelength, frequency aur photon energy, lagbhag same size ki ek cheez, aur aisi waves kaise banti, detect hoti aur use hoti hain, yeh sab dikhta hai. Visible region mein ek swatch colour dikhata hai.

Fig. 8.13Bar par drag karo, koi example tap karo ya frequency, wavelength ya photon energy type karo aur dekho ki woh kahan aati hai.

Table 8.4Ek nazar mein electromagnetic spectrum (boundaries approximate hain)

Region	Wavelength	Photon energy	Ek example source	Ek example use
Radio	$0.1 m$ se zyada	$1.2 \times 10^{- 5} e V$ se kam	antenna mein oscillate karte charges	broadcasting, mobile phones
Microwave	$1 m m$ se $0.1 m$	$1.2 \times 10^{- 5}$ se $1.2 \times 10^{- 3} e V$	magnetron	radar, ovens, Wi-Fi
Infrared	$700 n m$ se $1 m m$	$1.2 \times 10^{- 3}$ se $1.8 e V$	garam body, infrared LED	remote controls, thermal cameras
Visible	$400 n m$ se $700 n m$	$1.8$ se $3.1 e V$	Sun, flame, LED	dekhna, photography, lighting
Ultraviolet	lagbhag $1 n m$ se $400 n m$	$3.1 e V$ se lagbhag $1 k e V$	Sun, welding arc, mercury lamp	paani disinfect karna, LASIK
X-rays	lagbhag $10^{- 4} n m$ se $10 n m$	kuch sau eV se MeV tak	metal target se takraate fast electrons	medical imaging, airport scanners
Gamma rays	lagbhag $0.1 n m$ se kam	lagbhag $10 k e V$ se zyada	cobalt-60 jaise radioactive nuclei	cancer therapy, sterilisation

8.4.1 Radio waves

Radio waves ki wavelengths lagbhag $10 c m$ se lekar kai kilometres tak hoti hain, yaani frequencies lagbhag $3 G H z$ se kam. Yeh antennas aur circuits mein aage-peeche accelerate hote charges se banti hain, bilkul Section 8.3.1 ki tarah. Radio region ko itni saari services share karti hain ki frequencies international agreement se baanti jaati hain; Table 8.5 inmein se kuch dikhata hai.

Table 8.5Kaun kaunsi radio frequencies use karta hai (approximate)

Service	Frequencies	Wavelengths
Medium-wave AM (kai All India Radio stations bhi)	$0.53$ se $1.6 M H z$	lagbhag $570 m$ se $190 m$
Short-wave broadcasting, jo continents ke paar sunai deti hai	$3$ se $30 M H z$	$100 m$ se $10 m$
FM radio	$88$ se $108 M H z$	$3.4 m$ se $2.8 m$
Television (VHF aur UHF channels)	lagbhag $50$ se $900 M H z$	$6 m$ se $0.33 m$
Satellite navigation (GPS; India ka NavIC)	lagbhag $1.2$ se $2.5 G H z$	$25 c m$ se $12 c m$
Mobile phones	lagbhag $0.7$ se $3.6 G H z$ , microwaves tak jaati hain	$43 c m$ se $8 c m$

Antenna sabse achha tab radiate karta hai jab uski length wavelength ke comparable ho, aksar uski aadhi ya chauthai. Isiliye car par FM antenna ek metre se chhota hota hai, jabki medium-wave transmitter ko das-das metre ooncha mast chahiye. Yahi rule of thumb poore spectrum mein chalta hai. Nikalne wali wavelength aksar usko nikaalne wali cheez ke size ke comparable hoti hai, antennas se lekar atomic nuclei tak, jaisa Fig. 8.12 mein cheezon ke size ishara karte hain. Atoms iske khaas exception hain: lagbhag $0.1 n m$ ke hote hue bhi woh hazaaron guna lambi visible light nikaalte hain.

Example

Tune karna

(a) $98.3 M H z$ par broadcast karne wale FM station ki wavelength nikaalo, aur uske liye quarter-wave antenna ki length bhi. (b) $819 k H z$ wale medium-wave station ke liye dohrao, aur result par comment karo.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

8.4.2 Microwaves

Tumhara kitchen aur tumhari pocket, dono microwaves use karte hain. Microwaves (सूक्ष्म तरंगें) radio region ke short-wavelength end par hain: lagbhag $1 m m$ se $10 c m$ , yaani $3$ se $300 G H z$ . Boundary dheeli hai, aur yeh naam aksar kuch das centimetre lambi waves tak bhi kheencha jaata hai, jaise microwave oven wali. Wi-Fi routers $2.4$ aur $5 G H z$ par kaam karte hain, satellite television dishes $11$ – $12 G H z$ ke aas-paas signals receive karti hain, aur naye mobile networks $3.3$ – $3.6 G H z$ use karte hain. Inhe banane ke liye khaas sources chahiye: magnetrons naam ki vacuum tubes, jo har microwave oven mein hoti hain, aur klystrons, jo bade radars aur satellite transmitters mein lagte hain, saath hi Gunn diodes jaise solid-state devices.

Chhoti wavelength ka ek bada fayda hai: sirf ek-do metre chaudi dish microwaves ko patli beam mein focus kar sakti hai. Isliye yeh radar ke liye perfect hain, jo ek chhota pulse bhejta hai aur uski echo ka time naapta hai. Air-traffic controllers isi tarah aircraft track karte hain, aur India Meteorological Department ke Doppler weather radars coast ki taraf aate cyclones ko follow karte hain.

Example

Echo ka time naapna

$5.6 G H z$ par chalne wala weather radar ek pulse bhejta hai aur storm cloud se echo $0.80 m s$ baad receive karta hai. (a) Cloud kitni door hai? (b) Radar waves ki wavelength kya hai?

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Microwave oven $2.45 G H z$ ki waves use karta hai, jinki wavelength lagbhag $12 c m$ hai. Water molecule ek electric dipole hai: oxygen wale end par thoda negative aur hydrogen wale end par thoda positive. Wave ka oscillating electric field in dipoles ko ek second mein arabon baar aage-peeche ghumata hai (Fig. 8.14). Ghoomte hue molecules apne padosiyon ko dhakka dete hain, aur wave se li gayi energy random thermal motion ban jaati hai: khana garam ho jaata hai. Tum padh sakte ho ki oven ki frequency water molecules ki natural frequency se match karne ke liye chuni gayi hai. Poori picture yeh hai ki paani microwave frequencies ki ek wide range mein strongly absorb karta hai; $2.45 G H z$ aise use ke liye alag rakha gaya band hai, aur yeh khane mein kuch centimetre andar tak jaata hai. Sookhe glass aur ceramic dishes bahut kam absorb karte hain aur thande rehte hain, jabki metals microwaves ko reflect karte hain.

1/3Water molecules electric dipoles hain: field har ek ko aise ghumata hai ki uska positive (hydrogen) end $𝐄$ ke along point kare.

Fig. 8.14Oscillating electric field polar water molecules ko ghumata rehta hai; unka aapas mein takraana wave energy ko heat mein badal deta hai.NCERT p. 209

Saat water molecules ek panel mein tair rahe hain, har ek mein ek bada red oxygen atom aur do chhote green hydrogen atoms; neeche ek key dikhati hai ki oxygen end negative aur hydrogen end positive hai. Left mein ek orange arrow microwaves ka electric field dikhata hai. Step 1: field upar point karta hai aur har molecule aise ghoom gaya hai ki uska hydrogen end upar hai. Step 2: field ulta hokar neeche point karta hai aur har molecule use follow karne ke liye ulta ho gaya hai. Step 3: field arrow double-headed ho jaata hai, ek second mein arabon baar palat-ta hai, molecules har direction mein point karte hain aur unke paas chhote motion marks hain, aur panel mein garam glow bhar jaata hai.

Quick check

3 mein se 1

Ek FM station

93.5 M H z

par broadcast karta hai. Uski waves ki wavelength kitni hai, metres mein?

Answer dekho

Answer 3.21 m

λ = c / ν = (3.0 \times 10^{8}) / (9.35 \times 10^{7}) = 3.21 m

8.4.3 Infrared waves

Garam tawa ya iron ke paas bina chhue khade ho, to tumhara chehra garam mehsoos hota hai. Jo tum tak pahunchta hai woh infrared (अवरक्त) radiation hai: visible spectrum ke red end ke thik aage ki waves, lagbhag $700 n m$ se $1 m m$ tak. Har garam cheez ise nikaalti hai, aur cheez jitni garam, utna zyada emit karti hai aur uski wavelengths utni chhoti hoti hain. Tumhari apni body $10 μ m$ ke paas sabse zyada glow karti hai, isiliye thermal camera andhere mein logon ko dhoondh leta hai.

Technology mein infrared har jagah hai. Remote controls $940 n m$ ke paas infrared light-emitting diodes use karte hain. Optical fibres internet traffic ko $1.3$ aur $1.55 μ m$ par le jaate hain, jahan glass sabse transparent hota hai. Night-vision aur thermal cameras ise detect karte hain, physiotherapists akdi muscles ko infrared lamps se garam karte hain, aur earth-observation satellites ise crops, forests aur paani ka map banane mein use karte hain.

Light ki jagah infrared garam kyun lagta hai? Iski frequencies un natural frequencies ke paas hain jin par molecules vibrate aur rotate karte hain. Paani, carbon dioxide aur kai doosre molecules ise strongly absorb karte hain, aur energy sirf electrons ko nahi balki poore molecules ko hilaane mein jaati hai; yaani woh heat ban jaati hai. Kyunki zyadatar materials mein kuch paani hota hai, zyadatar materials infrared mein garam ho jaate hain, isiliye ise aksar heat radiation kehte hain.

Yahi absorption hamare planet ko rehne laayak banaye rakhta hai. Greenhouse gases ke bina Earth ki surface ka average lagbhag −18 °C hota; asal mein yeh lagbhag +15 °C hai. Yeh fark greenhouse effect hai (Fig. 8.15). Hawa aane wali zyadatar sunlight ko zameen tak jaane deti hai jisse zameen garam hoti hai, lekin garam zameen infrared wavelengths par radiate karti hai, jinhe water vapour aur carbon dioxide absorb karke kuch hissa wapas neeche bhejte hain.Hawa mein carbon dioxide badhane se greenhouse effect strong hota hai, aur yahi aaj ki global warming ki main wajah hai.

3/3 $C O_{2}$ aur $H_{2} O$ molecules us infrared ka kuch hissa absorb karke har direction mein dobara emit karte hain, kuch wapas neeche: yahi greenhouse effect hai.

Fig. 8.15Atmosphere zyadatar sunlight ko andar aane deta hai lekin garam zameen jo infrared wapas bahar bhejti hai uska kuch hissa absorb kar leta hai.NCERT p. 210

Sun top left mein hai, atmosphere ki ek halki blue patti beech se guzarti hai aur green zameen neeche phaili hai. Step 1: chhoti wavelengths wale teen orange wavy arrows, jin par visible likha hai, Sun se seedhe atmosphere paar karke zameen tak jaate hain. Step 2: zameen garam rang le leti hai aur usse kahin lambi wavelengths wale teen red wavy arrows, jin par infrared likha hai, atmosphere se upar uthte hain. Step 3: ek red arrow ab bhi space mein nikal jaata hai, lekin baaki do atmosphere mein ek carbon dioxide molecule aur ek water molecule par khatam hote hain, jo naye red arrows wapas neeche zameen ki taraf aur ek upar bhejte hain.

Ghar par try karo

Apne remote control ki light dekho

Tumhe chahiye

TV ya air-conditioner ka remote control
camera wala phone

Pehle guess karo

Tum remote ke bulb ko seedha dekhte ho aur button dabate ho. Tumhe kya dikhta hai?

Kuch bhi nahiChamakti hui red lightSteady white glow

TV ya air-conditioner ke remote ko apni aankh ki taraf (thodi doori se) karo aur button dabao. Uske aage ke chhote bulb ko dekho.
Ab button dabate hue usi bulb ko apne phone ki camera screen par dekho.
Front (selfie) camera aur rear camera dono se try karo. Kya ek mein flashes zyada bright dikhte hain?

8.4.4 Visible rays

Spectrum ka sirf ek hissa hum seedhe mehsoos karte hain, aur woh ek patli band hai: ek end par $700 n m$ ( $4.3 \times 10^{14} H z$ ) ke paas red light, doosre par $400 n m$ ( $7.5 \times 10^{14} H z$ ) ke paas violet. Sunlight, flames, garam filaments aur LEDs sab ise tab banate hain jab atoms, molecules aur solids ke electrons energy chhod kar lower energy levels par girte hain.

Hamari aankhein yahi band kyun use karti hain, koi aur kyun nahi? Atmosphere se guzar kar zameen tak pahunchne wali sunlight mein visible wavelengths sabse zyada hoti hain, aur insaani aankhein $555 n m$ ke paas, yellow-green mein, sabse sensitive hoti hain, jo us output ke beech ke kareeb hai. Aankhein sabse zyada milne wali light ka poora fayda uthane ke liye evolve hui. Doosre jaanwar alag slice dekhte hain. Reindeer ultraviolet dekhte hain, jisse lichen aur bhediye barf par alag dikhte hain, aur vampire bats apne shikaar ki skin ke paas ki blood vessels ki infrared garmi mehsoos karte hain.

8.4.5 Ultraviolet rays

Violet end ke aage ultraviolet (पराबैंगनी) radiation hai, jo lagbhag $1 n m$ wavelengths par X-rays mein mil jaata hai. Humein milne wala sabse bada source Sun hai, lekin welding arcs, mercury-vapour lamps aur doosre bahut garam sources bhi ise emit karte hain. Iske photons chemical bonds todne layak energy le jaate hain (photon energies dekho), isliye iske effects wavelength par bahut depend karte hain. Living cheezon ke liye ise aksar teen bands mein baanta jaata hai, jinki tulna Table 8.6 mein hai.

Table 8.6Ultraviolet ke teen bands

Band	Wavelength	Photon energy	Sunlight mein iska hissa	Effects aur uses
UV-A	$315$ – $400 n m$	$3.1$ – $3.9 e V$	zyadatar zameen tak pahunchta hai; window glass se kuch guzar jaata hai	tanning, skin ka budhapa; banknote ke security marks ko chamkaata hai
UV-B	$280$ – $315 n m$	$3.9$ – $4.4 e V$	zyadatar ozone absorb karti hai; window glass rok leta hai	sunburn aur skin-cancer ka risk; skin ko vitamin D banane mein madad karta hai
UV-C	$100$ – $280 n m$	$4.4$ – $12 e V$	ozone aur hawa poori tarah absorb kar lete hain	$254 n m$ ke paas germicidal lamps paani aur hawa ko disinfect karte hain

Ultraviolet useful bhi hai aur harmful bhi. LASIK eye surgery mein ultraviolet laser ke pulses cornea ki shape badalte hain, ek baar mein micrometre ka chhota sa hissa tissue hatate hue. Chhoti wavelength se bahut fine focus milta hai, aur energetic photons aas-paas ke tissue ko garam kiye bina bonds tod dete hain. Nuksaan se bachne ke kai shields hain. Ultraviolet mein aayi skin extra melanin banati hai, ek dark pigment jo radiation ko gehre cells tak pahunchne se pehle absorb kar leta hai; tan iska dikhne wala sign hai. Window glass UV-B absorb karta hai, isliye band khidki sunburn rokti hai, aur ultraviolet nikaalne wale arc ke saamne kaam karne wala welder special dark glass ke visor se dekhta hai.

Sabse bada shield stratosphere mein, kuch das kilometre upar, ozone layer hai, jo UV-C aur zyadatar UV-B ko humse door rakhti hai. Puraane refrigerators aur aerosol sprays ke chlorofluorocarbons (CFCs) ise khatam karte paaye gaye. Duniya ne 1987 ke Montreal Protocol mein inhe dheere-dheere band karne par sahmati di, jismein India 1992 mein juda. Layer ab dheere-dheere theek ho rahi hai.

Quick check

3 mein se 1

Infrared ko heat radiation kehne ki main wajah kya hai?

Yeh sirf 100 °C se zyada garam cheezein nikaalti hainYeh light se slow chalta hai isliye zyada energy deta haiYeh poore molecules ko vibrate karata hai, jisse unki internal energy badhti haiIse sirf metals absorb karte hain

Answer dekho

Answer (C) Yeh poore molecules ko vibrate karata hai, jisse unki internal energy badhti hai

Infrared frequencies molecular vibrations se match karti hain, isliye absorb hua infrared thermal energy ban jaata hai. Har garam cheez, lagbhag 37 °C par tum bhi, infrared nikaalti hai, aur yeh light ki speed se hi chalta hai.

8.4.6 X-rays

Wilhelm Röntgen ne 1895 mein evacuated glass tubes se electric discharges guzarte hue X-rays discover ki. Aaj ke spectrum par yeh lagbhag $10 n m$ aur $10^{- 13} m$ ( $10^{- 4} n m$ ) ke beech hain, ek taraf ultraviolet aur doosri taraf gamma rays se overlap karti hui. Modern X-ray tube (Fig. 8.16) garam filament se electrons nikaalti hai, unhe das-das kilovolts ke potential difference se accelerate karti hai, aur unhe tungsten jaise metal target mein achanak rok deti hai. Tezi se decelerate hue electrons X-rays radiate karte hain, aur target atoms ke inner shells se nikale gaye electrons khaas wavelengths ki X-rays jodte hain.

4/4Electrons target mein ruk jaate hain. Achanak deceleration, aur target atoms ke inner shells mein electron jumps, X-rays banate hain.

Fig. 8.16X-ray tube mein fast electrons metal target mein achanak ruk jaate hain, aur unki energy ka kuch hissa X-rays ban kar nikalta hai.NCERT p. 211

Figure ke across ek sealed glass tube padi hai. Left mein ek coiled filament hai, negative electrode; right mein tirchi target face wala metal block, positive electrode. Dono se wires upar ek high-voltage supply tak jaati hain jo battery symbol ki tarah bani hai. Step 1: filament thanda aur andhera hai aur kuch nahi hota. Step 2: filament red chamakta hai aur uske paas blue electrons ka ek chhota cloud jama hota hai. Step 3: electrons tube ke across target ki taraf bhaagte hain, jise dots ki row aur ek arrow dikhate hain. Step 4: bahut chhoti wavelengths wale purple wavy arrows target face se nikal kar tube ke neeche se bahar jaate hain, jin par X-rays likha hai.

X-rays soft tissue se aasaani se guzar jaati hain lekin haddi unhe strongly absorb karti hai, kyunki haddi ke calcium atoms flesh ke hydrogen, carbon aur oxygen atoms se bhaari hote hain. Yahi contrast skeleton ki jaani-pehchani shadow picture deta hai, aur CT scanners aisi kai pictures ko milakar three-dimensional images banate hain. X-rays airports par luggage screen karti hain, crystals mein atoms ki arrangement dikhati hain, aur zyada doses mein cancer cells ko khatam karti hain. Wahi energy healthy cells ko bhi nuksaan pahunchati hai, isliye exposure jitna ho sake kam rakha jaata hai: technicians shielding ke peeche khade hote hain, aur patients jin hisson ki jaanch nahi ho rahi un par lead aprons pehente hain.

8.4.7 Gamma rays

Atoms ki tarah atomic nuclei ke bhi energy levels hote hain, lekin woh lagbhag ek million guna zyada door-door hote hain. Jab nucleus radioactive decay ya nuclear reaction mein lower level par girta hai, to woh gamma rays ka ek photon nikaalta hai, jo Fig. 8.12 ka sabse energetic region hai. Inki wavelengths lagbhag $10^{- 10} m$ se $10^{- 14} m$ se bhi kam tak hoti hain, yaani khud nucleus ke size tak. Gamma rays space ki zabardast events se bhi hum tak aati hain, jaise phat-te stars se. Inki penetrating power inhe useful banati hai. Hospitals mein cobalt-60 sources ki beams tumours par daali jaati hain taaki cancer cells khatam hon, aur gamma radiation syringes, gloves aur doosri supplies ko unke sealed packets ke andar hi sterilise karta hai.

Compare

X-rays aur gamma rays

X-rays

Electrons se aati hain: tez deceleration, ya inner atomic shells ke beech jumps
Photon energies aksar lagbhag $0.1$ se kuch sau keV
X-ray tubes mein zaroorat ke hisaab se banayi jaati hain

Gamma rays

Atomic nuclei se aati hain: radioactive decay aur nuclear reactions
Photon energies aksar das-das keV se kai MeV tak
Cobalt-60 jaise radioactive sources nikaalte hain

Jahan dono ranges overlap karti hain, wahan same wavelength ki X-ray aur gamma ray bilkul ek hi tarah ki wave hain; alag naam sirf yeh batate hain ki woh kahan se aayi.

Sirf frequency mein alag waves itna alag behave kyun karti hain? Chapter 11 dikhayega ki radiation photons naam ke packets mein emit aur absorb hota hai, har ek energy $E = h ν$ le jaata hai, jahan $h = 6.63 \times 10^{- 34} J s$ Planck's constant hai. Electronvolts ( $1 e V = 1.6 \times 10^{- 19} J$ ) mein naapne par ek kaam ka form hai

Photon energy

E = h ν = \frac{h c}{λ} \approx \frac{1240 e V n m}{λ}

FM radio ka photon ek electronvolt ke millionth hisse se bhi kam energy le jaata hai, jo kisi bhi single molecule par asar daalne ke liye bahut kam hai. Radio waves aur microwaves matter par apne fields ke kai charges par mile-jule push se kaam karte hain. Visible light ke photons, lagbhag $2$ se $3 e V$ , atoms aur molecules ke outer electrons ki energies se match karte hain, isiliye light vision aur photosynthesis chala sakti hai. Ultraviolet photons mein chemical bonds todne layak energy hoti hai. X-ray photons, hazaaron electronvolts, bhaari atoms ke inner electrons se aate hain, aur gamma-ray photons, millions of electronvolts, nuclei ke andar ki rearrangements se. Photons ki energy unhe nikaalne wale system ke energy scale ko dikhati hai.

Example

Poore spectrum mein photon energies

Ek photon ki energy electronvolts mein nikaalo: (a) $100 M H z$ par FM radio, (b) $2.45 G H z$ par microwave oven, (c) $530 n m$ wavelength ki green light, (d) $254 n m$ par germicidal lamp, (e) $0.10 n m$ wavelength ki X-rays aur (f) $1.0 \times 10^{- 12} m$ wavelength ki gamma rays. $h = 6.63 \times 10^{- 34} J s$ , $1 e V = 1.6 \times 10^{- 19} J$ aur $h c \approx 1240 e V n m$ lo.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Quick check

4 mein se 1

Inhe photon energy badhne ke order mein lagao.

Visible light
Ultraviolet
X-rays
Microwaves
Gamma rays
Infrared
Radio waves

Answer dekho

Answer

Radio waves
Microwaves
Infrared
Visible light
Ultraviolet
X-rays
Gamma rays

Photon energy

E = h ν

frequency ke saath badhti hai, isliye yeh order frequency badhne ka order hai, jo wavelength ghatne ka order hai.

Flash cards · 9

Key relations

1 / 9

Recap

Summary aur key points

Charging capacitor ke liye Ampère's law contradictory answers deta hai. Maxwell ne displacement current $i_{d} = ε_{0} d Φ_{E} / d t$ jod kar yeh contradiction hataya (Section 8.2).
Ampère–Maxwell law: $\oint 𝐁 \cdot d 𝐥 = μ_{0} i_{c} + μ_{0} ε_{0} d Φ_{E} / d t$ . Displacement current bilkul conduction current ki tarah magnetic field banata hai, aur jahan bhi electric field badalta hai wahan hota hai, vacuum mein bhi (Law).
Charging current $i$ wali radius $R$ ki circular plates ke beech rim ke andar $B = μ_{0} i r / 2 π R^{2}$ aur bahar $μ_{0} i / 2 π r$ hota hai (Derivation).
$𝐄$ aur $𝐁$ ke Gauss's laws, Faraday's law aur Ampère–Maxwell law, Lorentz force ke saath, poore classical electromagnetism ko describe karte hain (Table 8.1).
Ruke hue ya uniform motion wale charges radiate nahi karte; accelerated charges karte hain. Oscillating charge apni hi frequency ki waves bhejta hai, aur energy source se aati hai (Section 8.3.1).
Hertz ne 1887 mein electromagnetic waves banayi aur detect ki aur unki speed naapi; J. C. Bose ne millimetre waves banayi aur Marconi ne Atlantic ke paar signals bheje (Fig. 8.7).
Electromagnetic waves transverse hain: $𝐄$ , $𝐁$ aur travel ki direction aapas mein perpendicular hain, aur $𝐄 \times 𝐁$ travel ke along hai. Plane wave ke liye $E_{y} = E_{0} \sin (k x - ω t)$ aur $B_{z} = B_{0} \sin (k x - ω t)$ (Section 8.3.2).
$k = 2 π / λ$ , $ω = 2 π ν$ aur $c = ω / k = ν λ = 1 / \sqrt{μ_{0} ε_{0}} \approx 3.0 \times 10^{8} m / s$ ; fields same phase mein hain aur $B_{0} = E_{0} / c$ (Derivation).
Material mein speed $v = 1 / \sqrt{μ ε}$ hoti hai; frequency nahi badalti aur wavelength usi proportion mein chhoti ho jaati hai ((8.11)).
Electric aur magnetic fields energy ka barabar hissa le jaate hain; average energy density $\frac{1}{2} ε_{0} E_{0}^{2}$ hai (Derivation).
Wavelength ghatne ke order mein spectrum radio waves, microwaves, infrared, visible light, ultraviolet, X-rays aur gamma rays se guzarta hai, bina kisi sharp boundary ke (Section 8.4).
Photon energy $E = h ν$ radio waves ke liye electronvolt ke lagbhag millionth hisse se badhkar gamma rays ke liye millions of electronvolts tak jaati hai, aur yahi tay karti hai ki har region matter ke saath kaise interact karta hai (photon energies).
Spectrum mein uses aur hazards alag-alag hain: ozone zyadatar solar ultraviolet absorb karti hai, infrared greenhouse effect chalata hai, aur X-rays aur gamma rays body ki imaging aur treatment karti hain lekin inhe kam se kam use karna chahiye (Section 8.4.5).

Practice · 17 questions

Practice questions answers ke saath (NCERT “Exercises”)

Questions 1–10 NCERT exercises wali skills hi naye situations aur numbers ke saath practice karate hain; questions 11–17 extra practice hain. $c = 3.0 \times 10^{8} m / s$ , $ε_{0} = 8.85 \times 10^{- 12} C^{2} N^{- 1} m^{- 2}$ , $μ_{0} = 4 π \times 10^{- 7} T m / A$ aur $h c \approx 1240 e V n m$ lo.

1
NumericalMediumNCERT Exercises 8.1
School laboratory mein do square aluminium sheets, har ek $20 c m \times 20 c m$ , patle plastic spacers se $4.0 m m$ door rakh kar ek air capacitor banaya gaya hai. Ek constant-current supply ise $60 m A$ se charge karti hai.
1. Iski capacitance kitni hai, picofarads mein?
  pF
  Answer dekho
  Answer 88.5 pF
  $C = ε_{0} A / d = (8.85 \times 10^{- 12}) (0.040) / (4.0 \times 10^{- 3}) = 8.85 \times 10^{- 11} F \approx 89 p F$ .
2. Plates ke beech potential difference kis rate se badhta hai, volts per second mein?
  V/s
  Answer dekho
  Answer 678000000 V/s
  $d V / d t = i / C = 0.060 / (8.85 \times 10^{- 11}) = 6.8 \times 10^{8} V / s$ .
3. Plates ke beech displacement current kitna hai?
  Solution dikhao
  $Φ_{E} = E A = (V / d) A$ , isliye $i_{d} = ε_{0} d Φ_{E} / d t = (ε_{0} A / d) d V / d t = C d V / d t = 60 m A$ , jo charging current ke barabar hai.
4. Charge ek plate mein jaata hai, lekin gap ko koi cross nahi karta. Kya plate par Kirchhoff's junction rule lagta hai?
  Solution dikhao
  Sirf conduction current ke liye nahi: $60 m A$ plate mein jaata hai aur kuch bahar nahi nikalta, isliye wahan charge jama hota hai. Agar gap ke across plate se nikalne wale displacement current ko bhi gina jaaye, to har instant par andar aane wala total current bahar jaane wale ke barabar hai, aur junction rule lagta hai.
2
NumericalHardNCERT Exercises 8.2
Ek school physics club displacement current ka magnetic field detect karna chahta hai. Woh $7.5 c m$ radius ki do circular brass discs se $150 p F$ ka capacitor banate hain. Ek audio signal generator ise $50 V$ (rms) aur $1.0 \times 10^{4} r a d / s$ (lagbhag $1.6 k H z$ ) angular frequency par chalata hai. Ek chhoti search coil plates ke beech unke common axis se $5.0 c m$ door rakhi jaayegi.
1. Leads mein kitna rms current behega, microamperes mein?
  µA
  Answer dekho
  Answer 75 µA
  $I_{rms} = ω C V_{rms} = (1.0 \times 10^{4}) (1.5 \times 10^{- 10}) (50) = 7.5 \times 10^{- 5} A = 75 μ A$ .
2. Yeh current plates ke beech displacement current se kaise compare karega?
  Dono har instant par barabar hainDono sirf tab barabar hain jab voltage zero hoDisplacement current hamesha chhota hota hai
  Answer dekho
  Answer (A) Dono har instant par barabar hain
  $i_{d} = ε_{0} d Φ_{E} / d t = C d V / d t$ , jo har instant par bilkul charging current hai; dono sinusoidal hain aur unka amplitude aur phase same hai.
3. Search coil ko kitne amplitude ka magnetic field detect karna padega, tesla mein?
  T
  Answer dekho
  Answer 1.89e-10 T
  Peak current $I_{0} = \sqrt{2} \times 75 μ A = 106 μ A$ hai. Rim ke andar $B_{0} = \frac{μ_{0}}{2 π} \frac{I_{0} r}{R^{2}} = (2.0 \times 10^{- 7}) \frac{(1.06 \times 10^{- 4}) (0.050)}{(0.075)^{2}} = 1.9 \times 10^{- 10} T$ . Yeh Earth ke field se lagbhag 250 000 guna kamzor hai, isiliye aise measurements mushkil hain.
Quick answerEasyNCERT Exercises 8.3
Kuch kilometre door girne wali bijli radio waves ki crackle (lagbhag $300 m$ lambi), visible light ki flash (lagbhag $500 n m$ ) aur, jaisa aircraft par le jaaye gaye instruments ne dikhaya hai, gamma rays (lagbhag $1 p m$ ) ke chhote bursts nikaalti hai. Hawa paar karke tumhari taraf aate hue crackle, flash aur gamma burst mein kya common hai?
Unki frequencyUnki speedUnki energy per photonUnhe receive karne ke liye zaroori antenna ka size
Answer dekho
Answer (B) Unki speed
Saari electromagnetic waves vacuum mein $c = 3.0 \times 10^{8} m / s$ se chalti hain, aur hawa mein lagbhag utni hi speed se, isiliye AM radio thik usi pal crackle karta hai jab tum flash dekhte ho. Unki frequencies, photon energies aur unke liye sahi detectors mein bahut bada fark hai.
4
Short answerEasyNCERT Exercises 8.4
Tumse seedhe east mein ek transmitter ka $75 M H z$ radio signal hawa mein west ki taraf tumhari taraf aata hai. $x$ ko east ki taraf, $y$ ko north ki taraf aur $z$ ko vertically upar lo.
1. Iske electric aur magnetic fields kin directions mein ho sakte hain? Agar transmitting antenna vertical hai, yaani $𝐄$ vertical hai, to jis instant $𝐄$ upar point karta hai us waqt $𝐁$ kis taraf point karta hai?
  Solution dikhao
  Dono fields travel ki east–west line ke perpendicular hain, isliye woh vertical north–south plane mein hain, ek doosre se right angle par aur same phase mein. Wave $- x$ ke along chalti hai, isliye $𝐄 \times 𝐁$ ko $- x$ ke along point karna chahiye. $𝐄$ ke $+ z$ ke along hone par iske liye $𝐁$ ko $+ y$ ke along hona chahiye, kyunki $\hat{𝐤} \times \hat{𝐣} = - \hat{𝐢}$ : jab $𝐄$ upar point karta hai to $𝐁$ north point karta hai, aur jab $𝐄$ neeche point karta hai to south.
2. Iski wavelength kitni hai, metres mein?
  m
  Answer dekho
  Answer 4 m
  $λ = c / ν = (3.0 \times 10^{8}) / (7.5 \times 10^{7}) = 4.0 m$ .
5
NumericalEasyNCERT Exercises 8.5
Air-traffic controllers pilots se $118 M H z$ aur $137 M H z$ ke beech VHF radio channels par baat karte hain. Iska corresponding wavelengths ka band kya hai?
1. Sabse lambi wavelength, metres mein:
  m
  Answer dekho
  Answer 2.54 m
  $λ = c / ν = (3.0 \times 10^{8}) / (1.18 \times 10^{8}) = 2.54 m$ .
2. Sabse chhoti wavelength, metres mein:
  m
  Answer dekho
  Answer 2.19 m
  $λ = (3.0 \times 10^{8}) / (1.37 \times 10^{8}) = 2.19 m$ . Band lagbhag $2.19 m$ se $2.54 m$ tak hai, FM band se thoda chhota.
6
Short answerEasyNCERT Exercises 8.6
Wi-Fi router ke antenna ke charges har second $5.0 \times 10^{9}$ baar oscillate karte hain.
1. Router kis frequency par radiate karta hai?
  Solution dikhao
  Oscillating charges wali hi: $5.0 \times 10^{9} H z = 5.0 G H z$ .
2. Unki wavelength kitni hai, centimetres mein?
  cm
  Answer dekho
  Answer 6 cm
  $λ = c / ν = (3.0 \times 10^{8}) / (5.0 \times 10^{9}) = 0.060 m = 6.0 c m$ , microwave region mein.
NumericalEasyNCERT Exercises 8.7
FM transmitter ke paas ek chhota search-coil probe paata hai ki wave ka magnetic field $42 n T$ amplitude se oscillate karta hai. Usi jagah ek electric-field probe kitna amplitude record karega, volts per metre mein?
V/m
Answer dekho
Answer 12.6 V/m
$E_{0} = c B_{0} = (3.0 \times 10^{8}) (4.2 \times 10^{- 8}) = 12.6 V / m$ .
8
NumericalMediumNCERT Exercises 8.8
Short-wave transmitter se kuch doori par uske $20 M H z$ signal ko hawa mein $+ y$ ke along chalti plane wave maana ja sakta hai. Iska electric field $z$ ke along point karta hai aur amplitude $75 V / m$ hai. Nikaalo:
1. $λ$ , metres mein:
  m
  Answer dekho
  Answer 15 m
  $λ = c / ν = (3.0 \times 10^{8}) / (2.0 \times 10^{7}) = 15 m$ .
2. $k$ , radians per metre mein:
  rad/m
  Answer dekho
  Answer 0.419 rad/m
  $k = 2 π / λ = 2 π / 15 = 0.419 r a d / m$ (check: $ω / c$ bhi yahi deta hai).
3. $ω$ , radians per second mein:
  rad/s
  Answer dekho
  Answer 125700000 rad/s
  $ω = 2 π ν = 2 π (2.0 \times 10^{7}) = 1.26 \times 10^{8} r a d / s$ .
4. $B_{0}$ , tesla mein:
  T
  Answer dekho
  Answer 2.5e-7 T
  $B_{0} = 75 / (3.0 \times 10^{8}) = 2.5 \times 10^{- 7} T$ .
5. $𝐄$ aur $𝐁$ ke expressions likho.
  Solution dikhao
  $E_{z} = (75 V / m) \sin [(0.419 r a d / m) y - (1.26 \times 10^{8} r a d / s) t]$ .
  $𝐁$ , $z$ aur $y$ dono ke perpendicular hai, isliye yeh $x$ ke along hai, $𝐄$ ke saath same phase mein. Kyunki $\hat{𝐤} \times \hat{𝐢} = \hat{𝐣}$ (travel ki direction), positive $E_{z}$ ke saath positive $B_{x}$ hota hai: $B_{x} = (2.5 \times 10^{- 7} T) \sin [(0.419 r a d / m) y - (1.26 \times 10^{8} r a d / s) t]$ .

Long answerMediumNCERT Exercises 8.9

$E = h ν = h c / λ$ use karke in sab ke liye photon energy electronvolts mein nikaalo: $30 m$ wavelength ki radio waves, $1.0 c m$ ke microwaves, $10 μ m$ ka infrared, $650 n m$ ki red light, $0.050 n m$ ki X-rays aur $2.0 p m$ ki gamma rays. Yeh energy scales har tarah ki radiation ke sources se kaise judi hain?

Solution dikhao

Table 8.7

Radiation	Wavelength (nm)	Photon energy	Typical source
Radio	$3.0 \times 10^{10}$	$4.1 \times 10^{- 8} e V$	circuits aur antennas mein currents
Microwave	$1.0 \times 10^{7}$	$1.2 \times 10^{- 4} e V$	ghoomte molecules, electronic oscillators
Infrared	$1.0 \times 10^{4}$	$0.12 e V$	garam bodies mein vibrate karte molecules
Red light	$650$	$1.9 e V$	atoms ke outer electrons ka level badalna
X-rays	$0.050$	$2.5 \times 10^{4} e V = 25 k e V$	bhaari atoms ke inner electrons, rukte hue fast electrons
Gamma rays	$2.0 \times 10^{- 3}$	$6.2 \times 10^{5} e V = 0.62 M e V$	atomic nuclei

Har energy use nikaalne wale system ke energy levels ki spacing se match karti hai. Radio waves circuit mein bahut saare electrons ke collective motion se aati hain, jahan har photon ki energy negligible hai. Microwave aur infrared photons molecules ki rotational aur vibrational energies se match karte hain, aur visible photons (kuch eV) outer electrons ke levels se. X-ray photons (keV) bhaari atoms ke tightly bound inner electrons se match karte hain, aur gamma-ray photons (MeV) nuclei ke andar ke energy levels se.

10
NumericalMediumNCERT Exercises 8.10
Do telephone towers ke beech $12 G H z$ microwave link ke horn antenna ke paas beam ke electric field ka amplitude $36 V / m$ hai. Beam ko hawa mein $c$ se chalti plane wave maano.
1. Waves kitni lambi hain, centimetres mein?
  cm
  Answer dekho
  Answer 2.5 cm
  $λ = c / ν = (3.0 \times 10^{8}) / (1.2 \times 10^{10}) = 0.025 m = 2.5 c m$ .
2. Peak par magnetic field kitna strong hai, tesla mein?
  T
  Answer dekho
  Answer 1.2e-7 T
  $B_{0} = E_{0} / c = 36 / (3.0 \times 10^{8}) = 1.2 \times 10^{- 7} T$ .
3. Ek cycle par average kiye gaye electric field mein per cubic metre stored energy ko magnetic field mein stored energy se compare karo.
  Solution dikhao
  ${\overset{ˉ}{u}}_{E} = \frac{1}{2} ε_{0} \overline{E^{2}} = \frac{1}{4} ε_{0} E_{0}^{2} = \frac{1}{4} (8.85 \times 10^{- 12}) (36)^{2} = 2.9 \times 10^{- 9} J / m^{3}$ .
  ${\overset{ˉ}{u}}_{B} = \overline{B^{2}} / 2 μ_{0} = B_{0}^{2} / 4 μ_{0} = (1.2 \times 10^{- 7})^{2} / (4 \times 4 π \times 10^{- 7}) = 2.9 \times 10^{- 9} J / m^{3}$ .
  General mein $B_{0}^{2} / 4 μ_{0} = E_{0}^{2} / (4 μ_{0} c^{2}) = \frac{1}{4} ε_{0} E_{0}^{2}$ , kyunki $c^{2} = 1 / μ_{0} ε_{0}$ , isliye dono hamesha barabar hote hain.
Quick answerEasy
Ek capacitor ac supply se juda hai. Uski plates ke beech hota hai
kisi bhi tarah ka current nahigap koodte electrons se bana conduction currentdisplacement current sirf us pal jab supply on ki jaati haidisplacement current jo har instant par leads ke current ke barabar hai
Answer dekho
Answer (D) displacement current jo har instant par leads ke current ke barabar hai
Plates ke beech electric field lagaatar badalta rehta hai, isliye $ε_{0} d Φ_{E} / d t$ zyada der zero nahi rehta aur har instant par leads ke current ke barabar hota hai. Koi electron gap cross nahi karta.
12
Quick answerEasy
Spectrum ke har region ko ek typical source se match karo.
Left mein koi item tap karo, phir right mein uska match.
Answer dekho
Answer
Radio waves : antenna mein oscillate karte charges
Microwaves : magnetron
Infrared : garam body
Visible light : atoms mein level badalte electrons
X-rays : metal target mein roke gaye fast electrons
Gamma rays : radioactive nuclei
List mein neeche jaane par sources chhote hote jaate hain aur unke energy levels door-door, circuits se molecules, atoms aur nuclei tak.
Quick answerMedium
Ek khaas radio frequency par ek non-magnetic liquid ka $ε_{r} = 2.56$ hai. Us frequency ki radio waves usmein kitni tezi se chalti hain, metres per second mein?
m/s
Answer dekho
Answer 187500000 m/s
$v = c / \sqrt{ε_{r}} = (3.0 \times 10^{8}) / 1.6 = 1.9 \times 10^{8} m / s$ .
Quick answerEasy
Constant speed se circle mein ghoomta electron radiate nahi karta, kyunki uski speed kabhi nahi badalti.
SahiGalat
Answer dekho
Answer Galat
Uski velocity ki direction badalti rehti hai, isliye woh (centre ki taraf) accelerate ho raha hai aur radiate karta hai. Yeh radiation circular particle accelerators mein ek pareshani hai aur synchrotrons mein X-rays ka useful source.
Quick answerMedium
Ek point par vacuum mein wave ka electric field $+ y$ ke along point karta hai aur magnetic field $- x$ ke along. Wave kis direction mein chal rahi hai?
$+ z$ $- z$ $+ x$ $- y$
Answer dekho
Answer (A) $+ z$
Wave $𝐄 \times 𝐁$ ke along chalti hai: $\hat{𝐣} \times (- \hat{𝐢}) = - (\hat{𝐣} \times \hat{𝐢}) = - (- \hat{𝐤}) = + \hat{𝐤}$ . Yeh $x$ ya $y$ ke along nahi chal sakti, kyunki fields travel ki direction ke perpendicular hain.
Quick answerEasy
Airport radar ko apne pulse ki echo ek aircraft se use bhejne ke $0.24 m s$ baad milti hai. Aircraft kitni door hai, kilometres mein?
km
Answer dekho
Answer 36 km
Pulse jaata hai aur wapas aata hai, isliye $d = c t / 2 = (3.0 \times 10^{8}) (2.4 \times 10^{- 4}) / 2 = 3.6 \times 10^{4} m = 36 k m$ .
Long answerHard
Ek classmate kehta hai ki displacement current sirf ek mathematical trick hai, kyunki capacitor ke gap ke across sach mein koi charge nahi chalta. Do evidence do jo dikhayein ki iske real physical effects hain.
Solution dikhao
Pehla, yeh ek real magnetic field banata hai. Charging capacitor ke gap ke around magnetic field ghoomta hai, aur plates ke rim se aage kisi distance par uski value wire se usi distance par field ke barabar hoti hai, bilkul jaisa Ampère–Maxwell law maangta hai. Doosra, iske bina Maxwell's equations electromagnetic waves predict nahi karte. Iske saath woh $1 / \sqrt{μ_{0} ε_{0}} = 3.0 \times 10^{8} m / s$ se chalti waves predict karte hain; Hertz ne aisi waves banayi aur detect ki, unki speed naapi, aur light ki speed paayi. Har radio, phone aur microwave oven empty space mein displacement current par hi depend karta hai.

Apna NCERT exercise question dhoondo

Hamare practice questions ncert.ai ke liye likhe gaye hain aur NCERT exercises ko follow karte hain. Apni textbook ke question se match karne wala question dhoondo; uska answer uske saath hai.

Tumhari NCERT textbook mein	Yahan practice question
NCERT Exercises 8.1	Practice Q1
NCERT Exercises 8.2	Practice Q2
NCERT Exercises 8.3	Practice Q3
NCERT Exercises 8.4	Practice Q4
NCERT Exercises 8.5	Practice Q5
NCERT Exercises 8.6	Practice Q6
NCERT Exercises 8.7	Practice Q7
NCERT Exercises 8.8	Practice Q8
NCERT Exercises 8.9	Practice Q9
NCERT Exercises 8.10	Practice Q10

Quick check: MCQs

Warm-up2 questions
8.2 Displacement current4 questions
Maxwell's equations1 question
8.3.1 Electromagnetic waves ke sources3 questions
8.3.2 Electromagnetic waves ka nature3 questions
8.3.2 Electromagnetic waves ka nature4 questions
8.4.2 Microwaves3 questions
8.4.5 Ultraviolet rays3 questions
8.4.7 Gamma rays4 questions

Glossary · 15

Key terms (English + Hindi)

Ampère–Maxwell lawऐम्पियर-मैक्सवेल नियमempiyar-maxwell niyam: $\oint 𝐁 \cdot d 𝐥 = μ_{0} i_{c} + μ_{0} ε_{0} d Φ_{E} / d t$ : currents aur changing electric flux magnetic fields banate hain.Chapter mein pehli baar yahan aaya →
antennaऐन्टेनाantenna: Aisa conductor jismein oscillating charges electromagnetic waves bhejte hain, ya waves unhe chalati hain.Chapter mein pehli baar yahan aaya →

conduction currentचालन धाराchalan dhara: Chalte charges se bana current, jaise wire mein electrons.Chapter mein pehli baar yahan aaya →

displacement currentविस्थापन धाराvisthapan dhara: Ampère–Maxwell law mein term $i_{d} = ε_{0} d Φ_{E} / d t$ : changing electric flux jo current ki tarah magnetic field banata hai, bhale hi koi charge na behe.Chapter mein pehli baar yahan aaya →

electromagnetic spectrumवैद्युतचुंबकीय स्पेक्ट्रमvaidyut-chumbakiya spectrum: Frequency ya wavelength ke hisaab se lagayi gayi electromagnetic waves ki poori range, radio waves se gamma rays tak.Chapter mein pehli baar yahan aaya →
electromagnetic waveवैद्युतचुंबकीय तरंगvaidyut-chumbakiya tarang: Oscillating electric aur magnetic fields ka self-sustaining pattern, jo ek doosre ke aur travel ki direction ke perpendicular hote hain, aur vacuum mein $c$ se chalta hai.Chapter mein pehli baar yahan aaya →

gamma raysगामा किरणेंgama kiranen: Sabse chhoti electromagnetic waves, jo atomic nuclei nikaalte hain.Chapter mein pehli baar yahan aaya →

infraredअवरक्तavrakt: Lagbhag $700 n m$ se $1 m m$ ki waves, jo garam cheezein nikaalti hain; yeh molecules ko vibrate karati hain aur isliye jo inhe absorb kare use garam karti hain.Chapter mein pehli baar yahan aaya →

Maxwell's equationsमैक्सवेल समीकरणmaxwell samikaran: Woh chaar laws (E aur B ke Gauss's laws, Faraday's law aur Ampère–Maxwell law) jo batate hain ki electric aur magnetic fields kaise bante hain.Chapter mein pehli baar yahan aaya →
microwavesसूक्ष्म तरंगेंsukshma tarangen: Chhoti radio waves, lagbhag $1 m m$ se $10 c m$ lambi (boundary dheeli hai), jo radar, ovens aur Wi-Fi mein use hoti hain.Chapter mein pehli baar yahan aaya →

photonफ़ोटॉनphoton: Electromagnetic energy $h ν$ ka ek packet.Chapter mein pehli baar yahan aaya →

radio wavesरेडियो तरंगेंradio tarangen: Lagbhag $10 c m$ se lambi electromagnetic waves, jo antennas aur circuits mein oscillate karte charges se banti hain.Chapter mein pehli baar yahan aaya →

ultravioletपराबैंगनीparabainganee: Lagbhag $400 n m$ se neeche $1 n m$ tak ki waves, jinmein chemical bonds todne layak energy hoti hai.Chapter mein pehli baar yahan aaya →

wave numberतरंग संख्याtarang sankhya: $k = 2 π / λ$ , wave ke along per unit distance phase ka change.Chapter mein pehli baar yahan aaya →

X-raysएक्स-किरणेंeks-kiranen: Lagbhag $10 n m$ se neeche $10^{- 13} m$ tak ki waves, jo fast electrons ko metal target mein rokne par banti hain.Chapter mein pehli baar yahan aaya →

8.1 Introduction

8.2 Displacement current

8.3 Electromagnetic waves

8.3.1 Electromagnetic waves ke sources

8.3.2 Electromagnetic waves ka nature

8.4 Electromagnetic spectrum

8.4.1 Radio waves

8.4.2 Microwaves

8.4.3 Infrared waves

8.4.4 Visible rays

8.4.5 Ultraviolet rays

8.4.6 X-rays

8.4.7 Gamma rays

Apna NCERT exercise question dhoondo

Quick check: MCQs

Tum chapter ke end tak pahunch gaye