CONCEPT OF DISPLACEMENT CURRENT :-

The current due to the flow of charges in a conductor is called as Conduction current which is given as

c

dQI

dt

While applying the Ampere’s circuital law to find magnetic field at a point outside a capacitor connected to atime-varying current, Maxwell noticed an inconsistency in the Ampere’s circuital law, therefore he suggested theexistence of an additional current, called by him, the displacement current to remove this inconsistency.

According to maxwell changing electric field intensity is equivalent to a current that current is known as displacementcurrent (Id) which is given as

0

E

d

dI =

dt E

0 00

d c

d d Q dQI = = = =I

dt dt dt

The value of conduction current is equal to displacement current,source is either AC or DC.

Example: When a capacitor is allowed to charge in an electric circuit, the current flows through connecting wires.As capacitor charges, charge accumulates on the two plates of capacitor and as a result, a changing electric fieldis produced across between the two plate of the capacitor which gives rise to displacement current

++++++

––––––

E

I=Id

I=Ic I=Ic

Maxwell formulated following four equations involving electric and magnetic fields, and their sources, the chargeand current densities. These equations are known as Maxwell’s equations.

(1) Gauss law in electrostatics :

0

QE.dA

...(i)

(2) Gauss law in magnetism : B.dA 0

...(ii)

(3) Faraday's law of electromagnetic induction :

BdE.dl

dt

...(iii)

(4) Maxwell - Ampere's circuital law : E

0 c d c 0 00

dB.dl I I I

dt

... (iv)

INTRODUCTION OF ELECTROMAGNETIC WAVES

A changing electric field produces a changing magnetic field and vice versa which gives rise to a transverse waveknown as electromagnetic waves.

The electromagnetic waves consist of sinusoidally time varying electric and magnetic field acting at right angles to

ELECTROMAGNETIC WAVES

each other oscillating in same phase as well as at right angles to the direction of propagation.

According to Maxwell’s theory that accelerated charges radiate electromagnetic waves.

Consider a charge oscillating with some frequency, which is an example of accelerating charge, this produces an

oscillating electric field in space, which produces an oscillating magnetic field, which in turn, is a source of

oscillating electric field, and so on. The oscillating electric and magnetic fields thus regenerate each other and the

wave propagates through the space. The frequency of oscillation of the electromagnetic wave naturally equals to

frequency of oscillation of the charge. The energy associated with the propagating wave comes at the expense of

the energy of the source i.e. the accelerated charge.

In the year 1865, Maxwell predicted the electromagnetic waves theoretically. According to him, an accelerated

charge sets up a magnetic field in its neighbourhood.

In 1887, Hertz produced and detected electromagnetic waves experimentally at wavelength of about 6m.

Neither stationary charges nor charges in uniform motion (steady currents) can be sources of electromagnetic

waves

PROPERTIES OF ELECTROMAGNETIC WAVES :-

In electromagnetic wave, electric field E

and magnetic field B

are perpendicular to each other and wave

propagates perpendicular to both in the direction of E B

.For example E

remains in + y-direction and B

along the + z-direction and the wave propagates in + x direction.

y 0E E sin( t kx) Z 0B B sin( t kx)

0E = peak value of electric field intensity B0 = peak value of magnetic field intensity

Ey

Bz

Z

X

Y

c

The EM wave travels with a speed equal to speed of light in vacuum, which is given as

0 rms

0 rms0 0

E E1c

B B 0rms

EE

2 0

rms

BB

2

EM waves do not require medium to travel but it can travel in medium also.

The energy of EM wave is associated with electric field as well as magnetic field. The average electric energy

density E(u ) is equal to average magnetic energy density B(u )

Average energy density of electric field 2E 0 0

1u E

4 Average energy density of magnetic field

20

B0

B1u

4

E Bu u

220

0 00

B1 1E

4 4

Total average energy density of EM wave 00

22 0

av 0

B1 1u = E =

2 2

EM waves are transverse in nature as the energy carriers E

& B

oscillates to the direction of propagation thereforeEM waves undergo all the phenomenon shown by transverse waves like Interference, Diffraction & Polarizationetc.

INTENSITY OF ELECTROMAGNETIC WAVE (I) :-

Intensity of EM wave at a particular place in space in defined as total energy passing per unit area per unit timeperpendicular to the direction of propagation.

tcx

Total energy of EM wave of a particular section is av avU u (Ax) u (Ac t)

Therefore the intensity of EM wave is given as

avav

u Ac tUI u c

A t A t

Also, 00

22 0

0

B1 1I= E c= c

2 2

LINEAR MOMENTUM OF ELECTROMAGNETIC WAVE (p) :-

The linear momentum is carried by the portion of EM wave as it has motion as well as energy, which is given as

U

pc

When EM wave or radiation strikes with a material, there will be change in momentum. If the initial linear momentum is p, and if the EM wave strikes with material surface and gets absorbed that is final

momentum is zero, therefore change in momentum will be U

p=p=c

If the EM wave strikes with material surface and gets reflected back that is final momentum is equal and opposite

to initial momentum, therefore change in momentum will be 2U

p=2p=c

FORCE AND PRESSURE ON MATERIAL SURFACE DUE TO EM WAVE :-

Whenever EM wave strikes with a material surface, it exerts force as well pressure called as radiation pressure onit.

When EM wave gets absorbed by the material surface-

Force on metallic surface is

p p U IA

Ft t c t c

U

IA t

U

IAt

Radiation Pressure on metallic surface is,F I

P= =A c

When EM wave gets reflected by the material surface-

Force on metallic surface is

p 2p 2U 2IA

Ft t c t c

Radiation Pressure on metallic surface is, F 2I

PA c

Roentgen discovered X-ray while performing experiment on electric discharge tube.

COOLIDGE METHOD FOR THE PRODUCTION OF X-RAY

To Produce X-ray Three Things are Required(i) Source of electron(ii) Means of accelerating these electron to high speed(iii) Target on which these high speed electron strike

– +V (in kV)

F

filament

c anode

target

T

W

windowX-ray

water

C

e–

e–

On the basis of mode of production x-ray spectrum is of following two types -

1. Continuous spectrum of X-ray

When high speed electron collide from the atom of target and passes close to the nucleus. There is coulombattractive force due to this electron is deaccelerated i.e. energy is decreased. The loss of energy during deaccelerationis emitted in the form of X-rays. X-ray produced in this way are called Braking or Bremstralung radiation and formcontinuous spectrum.

+

12mv2

2

12mv1

2

M

LK

hX-ray

photon

v1

v2

e–

e–

In continuous spectrum of X-ray all the wavelength of X-ray are present but below a minimum value of wavelength

there is no X-ray. It is called cut off or threshold or minimum wavelength min( ) of X-ray. The minimum wavelength

depends on applied potential.

There will be a minimum wavelength of continuous X ray corresponding to total lose of K.E gained by thermions.

K.E gained by thermions if they are accelerated through a voltage 0V

E = eVo

X-RAYS

Energy of X ray photon = Loss in K.E of thermions

hc

E

max

min

hcE

minmax

hcE min

o

hceV

0

min0

12375= A

V (involts)

2. Characteristic Spectrum of X-ray

When highly accelerated electron strike with the atom of target then it knockout the electron of orbit, due to thisa vacancy is created. To fill this vacancy electron jump from higher energy level and electromagnetic radiation areemitted which form characteristic spectrum of X-ray.

+

M

LK

h

X-ray

photone–

e–

e–

The wavelength of characteristic X-ray depend on nature of target and not on applied potential

N

M

L

K

O

L seriesL L L

MMM

NN

4

3

2

1KKK K

K series

M series

N series

CORRESPONDING ENERGY : K K KE E E

L LE E

WAVELENGTH : K K K

L L

INTENSITY : K K KI I I

L LI I

0.02 0.04 0.06 0.08 0.10 0.12

1

2

3

rela

tive

inte

nsity

wavelength (nm)

X-ray from a molybdenum target at 35 kV

Bremsstrahlungcontinuum

characteristic X-ray

MOSELEY'S LAW :-

Moseley studied the characteristic spectrum of number of many elements and observed that the square root of thefrequency of a K-line is closely proportional to atomic number of the element. This is called Moseley's law.

= a(Z - b)

Z = atomic number of target,n = frequency of characteristic spectrumb = screening constant (for K- series b=1, L series b=7.4),a = proportionality constant

BRAGG’S LAW (DIFFRACTION OF X-RAY) :-

Diffraction of X-ray is possible by crystals because the interatomic spacing in a crystal lattice is order of wavelengthof X-rays it was first verified by Lauve.

Diffraction of X-ray take place according to Bragg's law

2dsin n

d

d = spacing of crystal plane or lattice constant or distance between adjacent atomic plane

= Bragg's angle or glancing angle = Diffracting angle n = 1, 2, 3 .......

For Maximum Wavelength of X-ray sin 1 , n = 1

therefore, max 2d

so if > 2d diffraction is not possible i.e. solution of Bragg's equation is not possible.

PROPERTIES OF X-RAY :-

X-ray always travel with the velocity of light in straight line because their wavelength is very small. X-ray is electromagnetic radiation it show particle and wave both nature In reflection, diffraction, interference, refraction and polarization X-ray shows wave nature while in

photoelectric effect it shows particle nature. There is no charge on X-ray thus these are not deflected by electric field and magnetic field. X-ray are invisible. X-ray affect the photographic plate When X-ray incident on the surface of substance it exert force and pressure and transfer energy and

momentum

DUAL NATURE OF RADIATION & MATTER

ELECTRON EMISSION :-

Metals have free electrons (negatively charged particles) that are responsible for their conductivity. The free electrons cannot normally escape out of the metal surface. If an electron attempts to come out of the

metal surface acquires a positive charges and pulls the electron back to the metal. A certain minimum energy is required to be given to electron to escape from metallic surface, which is called work

function. The work function is generally measured in electron-volt(eV) 191eV 1.6 10 J

The emission of free electron occurs by one of the following processes(a) THERMIONIC EMISSION:

By suitably heating, sufficient thermal energy can be imparted to the free electrons to enable them to come outof the metallic surface.

The emitted electrons are called as thermions or thermoelectrons.(b) FIELD EMISSION:

BY applying a very strong field (in order of 810 V / m ) to a metal, electrons can be pulled out of the metal dueto force by electric field.(c) PHOTOELECTRIC EMISSION:

When light of suitable frequency illuminates a metal surface, electrons are emitted from the metal surfaces. These photo(light)-generated electrons are called as photoelectrons. Photoelectric emission was discovered by Heinerich Hertz(1857-1894) Photoelectric effect was investigated by Hallwachs & Lenard.

PARTICLE NATURE OF LIGHT: THE PHOTON

In interaction of radiation with matter, radiation behaves as if it is made up of particles or packet of energycalled as photons or quantum.

About Photon: Rest mass of photon 0m0

Net charge on photon 0q speed of photon v = c(speed of light)

Energy of photon

hc

hE Also, 0)Ain(

1240E

Linear momentum corresponding to energy of photon

h

p

All photons of light of a particular frequency or wavelength have same energy and momentum, whatever is theintensity of radiation. By increasing the intensity of light of given frequency or wavelength, there is only an increasein number of per second crossing per unit area i.e. photon energy is independent of intensity of radiation.

Photons are electrically neutral and are not deflected by electric and magnetic fields. In a photon-particle collisions like photon-electron collision, the total energy and momentum are conserved but

the number of photons may or may not be conserved in a collision(as photons may be absorbed or new photonsmay be created)

THRESHOLD FREQUENCY 0

It is the minimum frequency of incidenting light below which, no emission of photoelectron occurs.

THRESHOLD WAVELENGTH 0λ It is the maximum wavelength of incidenting light above which emission of photoelectron does not occur. The energy of photon of threshold frequency or threshold wavelength is equal to work function of metal.

0

0

hcw h

EINSTEIN’S EQUATIONS FOR PHOTOELECTRIC EFFECT :-

Einstein explained P.E.E. on the basis of quantum theory, for which he was awarded nobel prize.

When light photons incident on metallic plate, at a time, only one photon can interact with one electron.

If energy of incidenting photon is less than work function of metal i.e. h W , no emission of photoelectronsoccurs.

If energy of incidenting photon h W then emission of photoelectrons may occur..

If the free electron of metallic surface absorbs all the energy of incidenting photon then energy equals to workfunction is used for just emission of electron & rest of the energy is carried as max K.E of photoelectron.

maxhv =W+K.E maxK.E hv W

0 2max

1mv =h h

2 o

2max

1 hc hcmv =

2

Einstein's Photo Electric equation is based on conservation of energy.

( )0 B

( )0 A

metal A metal B

(K)max

frequency

PHOTOCURRENT/PHOTOELECTRIC CURRENT (IP) :-

when the potential of collecting plate is zero then some of the energetic photoelectrons are able to reach atcollecting plate and a small current called as photocurrent is formed.

Photoelectric current p

charg eI

time =

Q

t = n

e e = 1.6 × 10–19 n

e

When a +ve potential is applied on collecting plate and is increased then the value of photocurrent increasesupto a maximum and constant value, this photocurrent is called as saturation current.

The value of saturation current depends upon intensity of incidenting light, not on frequency or wavelength ofincidenting light.

STOPPING POTENTIAL (Vo) :-

When ve potential is applied on collecting plate the photoelectrons get repelled by collecting or facing plates. For a particular ve potential of collecting plate the photoelectrons are emitted but reabsorbed by emitter plate or

in other words the maximum K.E of photoelectron is destroyed against this potential, this ve potential of facingplate is called as stopping potential.

Loss in max K.E = W.D against stopping poter

2max o

1mv eV

2

Therefore Einstein’s equation can be also written as

0 0eV =h h0

0hc hc

eV =

( )0 B

( )0 A

metal A metal B

V0

frequency

The value of stopping potential depends on frequency or wavelength of incidenting light not on the intensity ofincidenting light as the max K.E of photoelectron is determined by energy of one photon.

EFFECT OF DIFFERENT FACTORS IN PHOTOELECTRIC EFFECT

(1) EFFECT OF CHANGE IN INTENSITY OF INCIDENTING LIGHT

If the intensity of incidenting light is increased keeping the frequency same

The number of photons incidenting per second increases but the energy of one photon remains same.

The number of photoelectrons emitted per second gets increased and the max K.E one photon remainssame.

The saturation current increases & stopping potential remain same & vice versa.

(2) EFFECT OF CHANGE IN FREQUENCY OF INCIDENTING LIGHT

If the frequency of incidenting light is increased keeping the intensity same

The energy of one photon increases but the no of photons incidenting per second remain same The max K.E of photoelectron increases but the number of photoelectrons emitted per sec remains same.

The ve value of stopping potential increases but the saturation current remains same

(3) EFFECT OF CHANGE IN DISTANCE OF LIGHT SOURCE FROM CATHODE PLATE

On increasing the distance of light source from cathode plate keeping the frequency constant-

The intensity of light incidenting on cathode plate decreases

2r

1I

The number of photons incidenting per second decreases but the energy of one photon remains same.

The number of photoelectrons emitted per second gets decreased and the max K.E one photon remainssame.

The saturation current decreases & stopping potential remain same & vice versa.

FAILURE OF WAVE THEORY OF LIGHT

(I) According to wave theory when light incident on a surface, energy is distributed continuously over the surface. Sothat electron has to wait to gain sufficient energy to come out. But in experiment there is no time lag.

(II) When intensity is increased, more energetic electrons should be emitted. So that stopping potential should beintensity dependent. But it is not observed.

(III) According to wave theory, if intensity is sufficient then, at each frequency, electron emission is possible. It meansthere should not be existence of threshold frequency.

NOTE :- Photoelectric effect dks wave nature of light ls explain ugha fd;k tk ldrk gSS D;ksafd wave dh energy amplitude c<+kdjds c<+kbZ tk ldrh gS vFkkZr~ low frequency ij high energy dh wave possible gS vkSj photoelectrons dk emission djk;ktk ldrk gS ysfdu P.E.E. djkus ds fy, incidenting light fd ,d minimum frequency(Threhold frequency) required gksrh gSA

MATTER WAVES

According to De Broglie some atomic and sub-atomic particle either charged or uncharged, like electron, neutronetc. show dual nature i.e particle nature as well as wave nature.

The wave associated with matter particle is called as Matter Wave or De-Broglie wave. The wavelength of such a wave is called as De-broglie wavelength which is given as

h h h

= = =p mv 2mE

h=planck’s constant m= mass of particle p= linear momentum E= K.E of particle

1 1 1

p v E

The wave nature of electron was first experimentally verified by Davisson & Germer. In their experiment the

electron beam gets diffracted by diffraction grating and follows Bragg’s law (n 2d sin )

The working of electron microscope is based on wave nature of electron.

The Heisenberg uncertainty principle is also explained by the matter wave picture.

1. De Broglie Wavelength for charged particle

If a charged particle is accelerated through a P.d Vo then gain in K.E of charged particle E = qVo

0

h=

2mqV

for electron :- 0

0

12.27A

V

for proton :- 0

0

0.286A

V Vo= in Volt

for deutron :- 0

0

0.202A

V

for - particle :- 0

0

0.101A

V

2. De Broglie Wavelength for Uncharged Particle [Neutron]

The neutron attains linear momentum by thermal agitation.

If neutron is in thermal equilibrium at ordinary temp

Gain in K.E E=kTk =Boltzmann consttT= Absolute temperature

0h 30.83A

2mkT T

If neutron is in thermal equilibrium with heavy water 3

E kT2

h h

3 3mkT2m kT

2

PROPERTIES OF MATTER WAVE

Matter waves are net electromagnetic in nature. Matter waves do not require medium travel The matter wave represents the probability of finding of particle in space. de Broglie wavelength is independent of charge

1. The charge on a parallel plate capacitor varies as 0q q cos 2 t. The plates are very large and close

together (area = A, separation = d). Thedisplacement current through the capacitor is

(A) 0q 2 sin t (B) 0q 2 sin 2 t

(C) 0q 2 sin t (D) 0q sin 2 t2. An electromagnetic wave can be produced, when

charge is(A) Moving with a constant velocity(B) Moving in a circular orbit(C) Falling in an electric field(D) Both (B) and (C)

3. If E and B denote electric and magnetic fieldsrespectively, which of the following is dimensionless?

(A) 0 0

EB (B) 0 0

EB

(C)

2

0 0

BE

(D)

0

0

EB

4. The electric field of an electromagnetic wave travellingthrough vacuum is given by the equation

0E E sin kx t . The quantity that is independent

of wavelength is

(A) k (B)k

(C) 2k (D) 5. The electric field part of an electromagnetic wave in

vacuum is

8N rad rad ˆE 3.1 cos 1.8 y 5.4 10 t i

C m s

The wavelength of this part of electromagnetic waveis(A) 1.5 m (B) 2 m(C) 2.5 m (D) 3.5 m

6. A parallel plate capacitor of capacitance 20 F isbeing charged by a voltage source whose potential ischanging at the rate of 3 V/s. The conduction currentthrough the connecting wires, and the displacementcurrent through the plates of the capacitor, wouldbe, respectively [NEET 2019](A) zero, zero (B) zero,60 A

(C) 60 A,60 A (D) 60 A,zero

7. For a transparent medium relative permeability andpermittivity, and are 1.0 and 1.44 respectively..The velocity of light in this medium would be

[NEET 2019]

(A) 82.5 10 m/ s (B) 83 10 m/ s

(C) 82.08 10 m/ s (D) 84.32 10 m/ s8. In an electromagnetic wave in free space the root

mean square value of the electric f ield is 1

rmsE 6Vm .The peak value of the magnetic fieldis [NEET 2017]

(A) 82.83 10 T (B) 80.70 10 T

(C) 84.23 10 T (D) 81.41 10 T

9. Light with an energy flux of 4 225 10 Wm falls on aperfectly reflecting surface at normal incidence. Ifthe surface area is 15 cm2, the average force exertedon the surface is [NEET 2014]

(A) 61.25 10 N (B) 62.50 10 N

(C) 61.20 10 N (D) 63.0 10 N10. The electric field of an electromagnetic wave in free

space is given by 7 ˆE 10cos 10 t kx j V / m

where t

and x are in seconds and metres respectively. It canbe inferred that [NEET 2010](1) the wavelength is 188.4 m.(2) the wave number k is 0.33 rad/m.(3) the wave amplitude is 10 V/m.(4) the wave is propagating along + x direction.Which one of the following pairs of statements iscorrect?(A) (3) and (4) (B) (1) and (2)(C) (2) adn (3) (D) (1) and (3)

11. The electric fields part of an electromagnetic wavein a medium is represented by Ex= 0;

6 2y

N rad radE 2.5 cos 2 10 t 10 xC m s ;

Ez = 0. The wave is [NEET 2009](A) moving along x direction with frequency106 Hz

and wavelength 100 m.(B) moving along x direction with frequency

106 Hz and wavelength 200 m.(C) moving along x direction with frequency

106 Hz and wavelength 200 m.(D) moving along y direction with frequency

62 10 Hz and wavelength 200 m

12. If 0 and 0 are the electric permittivity and magneticpermeability in a free space and are thecorresponding quantities in medium, the index ofrefraction of the medium is [NEET 1997]

(A) 0 0 (B)

0 0

EXERCISE- I (Daily Lecture Folio)

(C)0

0

(D)

0

13. In an electromagnetic wave,E = 1.2 sin(2 106 t kx)N/C.Find value of intensity of magnetic field.

[AIIMS 2016](A) 4 10-8 A/m (B) 0.1 10-2A/m

(C) 0.4 10-2 A/m (D)

210A/m

14. A plane electromagnetic wave is incident on amaterial surface. The wave delivers momentum pand energy E.(A) p = 0, E 0(B) p 0, E = 0(C) p 0, E 0(D) p = 0, E = 0.

15. Speed of electromagnetic waves is the same(A) for all wavelength (B) in all media(C) for all intensities (D) for all frequencies

16. The work function of a metal is hv0. Light offrequency v falls on this metal. The photoelectriceffect will take place only if(A) v v0 (B) v > 2v0

(C) v v0 (D) v < v0 /2

17. When stopping potential is applied in an experimenton photoelectric effect, no photocurrent is observed.This means that(A) the emission of photoelectrons is stopped(B) the photoelectrons are emitted but are

reabsorbed by the emitter metal(C) the photoelectrons are accumulated near the

collector plate(D) the photoelectrons are dispersed from the sides

of the apparatus.

18. A point source causes photoelectric effect from asmall metal plate. Which of the following curves mayrepresent the saturation photocurrent as a functionof the distance between the source and the metal ?

(A) a (B) b(C) c (D) d

19. Photoelectric effect supports quantum nature of lightbecause(A) there is a minimum frequency below which no

photoelectrons are emitted(B) the maximum kinetic energy of photoelectrons

depends only on the frequency of light and noton its intensity

(C) even when the metal surface is faintlyilluminated the photoelectrons leave the surfaceimmediately

(D) electric charge of the photoelectrons isquantized

20. A photon of energy hv is absorbed by a free electron

of a metal having work function hv(A) The electron is sure to come out(B) The electron is sure to come out with a kinetic

energy hv(C) Either the electrons does not come out or it

comes out with a kinetic energy hv(D) It may come out with a kinetic energy less than

hv21. The collector plate in an experiment on photoelectric

effect is kept vertically above the emitter plate. Lightsource is put on and a saturation photocurrent isrecorded. An electric field is switched on which hasvertically downward direction(A) The photocurrent will increase(B) The kinetic energy of the electrons will increase(C) The stopping potential will decrease(D) The threshold wavelength will increase

22. In which of the following situations the heavier ofthe two particles has smaller be Broglie wavelength?The two particles(A) move with the same speed(B) move with the same linear momentum(C) move with the same kinetic energy(D) have fallen through the same height

23. An electron of mass m with an initial velocity

0 0ˆV V i V 0

enters an electric field 0

ˆE E i

(E0 = constant > 0) at t = 0. If 0 is its de-Brogliewavelength initially, then its de-Broglie wavelengthat time t is [NEET 2018]

(A)

0

0

0

eE1 t

mV

(B)0

00

eE1 t

mV

(C) 0 t (D) 0

24. The stopping potential for photoelectrons from ametal surface is V1 when monochromatic light of

frequency 1 is incident on it. The stopping potentialbecomes V2 when monochromatic light of anotherfrequency is incident on the same metal Surface. Ifh be the planck’s constant and e be the charge of anelectron, then frequency of light in the second caseis [NEET 2009]

(A) 1 2 1

ev V V

h (B) 1 2 1

ev V V

h

(C) 1 2 1

ev V V

h (D) 1 2 1

ev V V

h

25. The figure shows a plot of photo current versus anodepotential for a photo sensitive surface for threedifferent radiations. Which one of the following is acorrect statement ?

abc

Retarding potential Anode potential

Photo current

1. A parallel plate capacitor with plate area A andseparation between the plates d, is charged by aconstant current I. Consider a plane surface of areaA/2 parallel to the plates and drawn between theplates. The displacement current through the area is

(A) I (B)I

2

(C)I

4(D)

I

82. A capacitor made of two circular plates each of

radius 12 cm and separated by 5 mm. The capacitoris being charged by an external source. The chargingcurrent is constant and equal to 0.15 A. thecapacitance of the parallel plate capacitor is

(A) 40 pF (B) 45 pF(C) 70 pF (D) 80 pF

3. Which among the following does not representMaxwell’s equation?

(A) 0

qE.dA

(B) B.dA 0

(C)

dBE.dl

dt

(D)

E0 C 0 0

dB.dl I

dt

4. If 0 be the permeability and 0 be the permittivityof a medium, then its refractive index is given by

(A) 0 0

1(B) 0 0

1

(C) 0 0 (D) 0 0

5. Electromagnetic wave consists of periodicallyoscillating electric and magnetic vectors(A) In mutually perpendicular planes but vibrating

with a phase difference of (B) In mutually perpendicular planes but vibrating

with a phase difference of 2

(C) In randomly oriented planes but vibrating inphase

(D) In mutually perpendicular planes but vibratingin phase.

6. The amplitude of an electromagnetic wave in vacuumis doubled with no other changes made to the wave.As a result of this doubling of the amplitude, whichof the following statement is correct ?(A) The speed of wave propagation changes only(B) The frequency of the wave changes only(C) The wavelength of the wave changes only(D) None of these.

7. A plane electromagnetic wave travels in free space

along X-direction. If the value of B

(in tesla) at a

particular point in space and time is 8 ˆ1.2 10 k, the

value of 1E in V m

at that point is

(A) ˆ1.2 j (B) ˆ3.6 k

(C) ˆ1.2k (D) ˆ3.6 j

8. Which of the following rays is not an electromagneticwave?(A) X-rays (B) -rays(C) -rays (D) Heat rays

(A) Curves (a) and (b) represent incident radiationsof different frequencies and different intensities

(B) Curves (a) and (b) represent incident radiationsof same frequency but of different intensities

(C) Curves (b) and (c) represent incident radiationsof different frequencies and different intensities

(D) Curves (b) and (c) represent incident radiationsof same frequency having same intensity

EXERCISE- II

9. An em wave is propagating in a medium with a

velocity ˆv vi. The instantaneous oscillating electric

field of this em wave is along +y axis. Then thedirection of oscillating magnetic field of the em wavewill be along [NEET 2018](A) z direction (B) + z direction(C) y direction (D) x direction

10. A 100 resistance and a capacitor of 100reactance are connected in series across a 220 Vsource. When the capacitor is 50% charged, the peakvalue of the displacement current is[NEET 2016](A) 2.2 A (B) 11A

(C) 4.4 A (D) 11 2 A

11. Out of the following options which one can be usedto produce a propagating electromagnetic wave ?

[NEET 2016](A) A charge less particle(B) An accelerating charge(C) A charge moving at constant velocity(D) A stationary charge

12. The energy of the em waves is of the order of 15keV. To which part of the spectrum does it belong?

[NEET 2015](A) Ultraviolet rays (B) -rays(C) X-rays (D) Infra-red rays

13. The condition under which a microwave oven heatsup a food item containing water molecules mostefficiently is [NEET 2013](A) Microwaves are heat waves, so always produce

heating.(B) Infra-red waves produce heating in a microwave

oven.(C) The frequency of the microwaves must match

the resonant frequency of the water molecules.(D) The frequency of the microwaves has no relation

with natural frequency of water molecules.

14. An electromagnetic wave of frequency 3.0MHz passes from vacuum into a dielectric

medium with relative permittivity 4.0 .Then [NEET 2013]

(A) Wavelength is doubled and frequency becomeshalf.

(B) Wavelength is halved and frequency remainsunchanged.

(C) Wavelength and frequency both remainunchanged.

(D) Wavelength is doubled and frequencyunchanged.

15. The electric field associated with an em wave in

vacuum is given by

8ˆE i 40 cos kz 6 10 t where

E, z and t are in volt/m, meter and seconds

respectively. The value of wave vector k is [NEET 2012]

(A) 12m (B) 10.5m

(C) 16m (D) 13m16. The ratio of amplitude of magnetic field to the

amplitude of electric field for an electromagneticwave propagating in vacuum is equal to

[NEET 2012](A) The speed of light in vacuum(B) Reciprocal of speed of light in vacuum(C) The ratio of magnetic permeability to the

electric susceptibility of vacuum(D) Unity

17. The decreasing order of wavelength of infrared,microwave, ultraviolet and gamma rays is

[NEET 2011](A) microwave, infrared, ultraviolet, gamma rays(B) gamma rays, ultraviolet, infrared, microwaves(C) microwaves, gamma rays, infrared, ultraviolet(D) infrared, microwave, ultraviolet, gamma rays

18. Which of the following statement is false for theproperties of electromagnetic waves ? [NEET 2010](A) Both electric and magnetic field vectors attain

the maxima and minima at the same placeand same time.

(B) The energy in electromagnetic wave is dividedequally between electric and magnetic vectors.

(C) Both electric and magnetic field vectors areparallel to each other and perpendicular to thedirection of propagation of wave.

(D) These waves do not require any materialmedium for propagation

19. If v x m, and represent the wavelengths of visiblelight, X-rays and microwaves respectively, then

[NEET 2005](A) m x v (B) m v x

(C) v x m (D) v m x

20. The electromagnetic waves do not transport(A) energy (B) charge(C) momentum (D) information

21. The wave function (in SI units) for an electromagneticwave is given as -

3 6 14(x, t) 10 sin (3 10 x 9 10 t) the speed ofthe wave is

(A) 149 10 m / s (B) 83 10 m / s

(C) 63 10 m / s (D) 73 10 m / s

22. For a wave propagating in a medium, identify theproperty that is independent of the others :-(A) velocity [AIIMS 2006](B) wavelength(C) frequency(D) All these depend on each other

[AIIMS 2015](A) 1 (B) 2(C) 0.5 (D) 0.25

31. In the EM wave the amplitude of magnetic field H0and the amplitude of electric field E0 at any placeare related as [AIIMS 2015]

(A) H0 = E0 (B) 00

EH

c

(C)

00 0

0

H E (D)

00 0

0

H E

32. Out of the following options which one can be usedto produce a propagating electromagnetic wave ?

[NEET 2016](A) A charge moving at constant velocity(B) A stationary charge(C) A charge less particle(D) An accelerating charge

33. In an electromagnetic wave the rms value of electricfield is 100 V/m. Find intensity of the wave.

[AIIMS 2016](A) 30.2 W/m2 (B) 15.3 W/m2

(C) 26.5 W/m2 (D) 15.7 W/m2

34. Electromagnetic wave of intensity 1400 W/m2 fallson metal surface on area 1.5 m2 is completelyabsorbed by it. Find out force exerted by beam.

[AIIMS 2016](A) 14 10-5 N (B) 14 10-6 N(C) 7 10-5 N (D) 7 10-6 N

35. A magnetic field can be produced by -(A) a moving charge(B) a changing electric field(C) none of them(D) both of them

36. An electromagnetic wave going through vacuum isdescribed byE =E0 sin(kx - wt); B = B0 sin(kx - wt). 0E E sin(kx t) ; 0B B sin(kx t)

Then(A) 0 0E k B (B) 0 0E B k(C) 0 0E B k (D) none ot these

37. An electric field E

and a magnetic field B

exist in aregion. The fields are not perpendicular to each other.(A) This is not possible(B) No electromagnetic wave may be passing

through the region(C) An electromagnetic wave may be passing

through the region.(D) An electromagnetic wave is certainly passing

through the region

23. The dimensions of 1/20 0( ) are :

[AIPMT 2011]

(A) 1/2 1/2[L T ] (B) 1[L T]

(C) 1[LT ] (D) 1/2 1/2[L T ]

24. The electric and magnetic field, associated with an

e. m. wave, propagating along the +z-axis, can be

represented by [AIPMT 2011]

(A) 0 0ˆ ˆ[E E i, B B j]

(B) 0 0ˆ ˆ[E E k, B B i]

(C) 0 0ˆ ˆ[E E j, B B i]

(D) 0 0ˆˆ[E E j, B B k]

25. The enegy of the em waves is of the order of 15 keV.To which part of the spectrum does it belong?

[Re AIPMT 2011](A) - rays (B) X - rays(C) Infra-red rays (D) Ultraviolet rays

26. A radiation of energy ‘E’ falls normally on a perfectlyreflecting surface. The momentum transferred to thesurface is (C = velocity of light) [AIPMT 2015]

(A)2EC

(B) 2

2EC

(C) 2

EC

(D)EC

27. A laser beam is of 9 mW, diameter = 2 mm. Thenwhat is the amplitude of magnetic field associatedwith it? [AIIMS 2015](A) 49 T (B) 98 T

(C) 9.8 T (D) 4.9 T

28. The intensity of sun on earth is 1400 W/m2. Assumingearth to be a black body. Calculate radiation pressure? [AIIMS 2015]

(A) 6 24.66 10 N / m (B) 6 21.6 10 N / m

(C) 6 24.66 10 N / m (D) 6 27 10 N / m

29. For an electromagnetic wave, [AIIMS 2015]

0 6 8

NE E sin 12 10 [Z 210 t]

Cin a medium, then its refractive index is

(A) 2/3 (B) 3/2

(C) 4/3 (D) 5/3

30. If velocity of an electromagnetic wave in a medium

is 3 108 m/s then find refractive index of medium.

38. A free electron is placed in the path of a planeelectromagnetic wave. The electron will start moving(A) along the electric field(B) along the magnetic field(C) along the direction of propagation of the wave(D) in a plane containing the magnetic field and

the direction of propagation

39. Displacement current goes through the gap betweenthe plates of a capacitor when the charge of thecapacitor(A) increases(B) decreases(C) does not change(D) is zero

40. The energy contained in a small volume throughwhich an electromagnetic wave is passing oscillateswith(A) zero frequency(B) the frequency of the wave(C) half the frequency of the wave(D) double the frequency of the wave

41. Two photons having(A) equal wavelengths have equal linear momenta(B) equal energines have equal linear momenta(B) equal frequencies have equal linear momenta(D) equal linear momenta have equal wavelength

42. Let p and E denote the linear momentum and energyof a photon. If the wavelength is decreased(A) both p and E increase(B) p increases and E decreases(C) p decreases and E increases(D) both p and E decrease

43. The equation E = pc is valid(A) for an electron as well as for a photon(B) for an electron but not for a photon(C) for a photon but nor for an electron(D) neither for an electron nor for a photon

44. Ligth of wavelength l falls on a metal having workfunction hc/l0. Photoelectric effect will take place onlyif(A) l l0 (B) l 2l0(C) l l0 (D) l < l0 /2.

45. The frequency and intensity of a light source areboth doubled, the stopping potential statements.(a) The saturation photocurrent remains almost thesame.(b) The maximum kinetic energy of the photoelectronsis doubled(A) Both (a) and (b) are true.(B) (a) is true but (b) is false(C) (a) is false but (b) is true(D) Both (a) and (b) are false

46. A proton and an electron are acceleration by thesame potential difference. Let le and lp denote thede Broglie wavelength of the electron and the protonrespectively

(A) e p

(B) e p

(C) e p

(D) The relation between le and lp depends on theacceleration potential difference

47. When the intensity of a light source is increased,(A) the number of photons emitted by the source

in unit time increases(B) the total energy of the photons emitted per unit

time increases(C) more energetic photons are emitted(D) faster photons are emitted

48. The photocurrent in an experiment on photoelectriceffect increases if(A) the intensity of the source is increased(B) the exposure time is increased(C) the intensity of the source is decreased(D) the exposure time is decreased

49. e p a, and are the de Broglie wavelengths ofelectron, proton and a particle. If all are acceleratedby same potential, then

(A) e p a (B) e p a

(C) e p a (D) e p a

50. If a proton and electron have the same de Brogliewavelength, then(A) Kinetic energy of electron < kinetic energy of

proton(B) Kinetic energy of electron = kinetic energy of

proton(C) Momentum of electron > momentum of proton(D) Momentum of electron < momentum of

proton51. A photon and an electron have equal energy E.

photon electron/ is proportional to [JEE 2004]

(A) E (B) 1 / E(C) 1 / E(D) Does not depend upon E

52. When the momentum of a proton is changed by anamount P0, the corresponding change in the de-Broglie wavelength is found to be 0.25%. Then, theoriginal momentum of the proton was [NEET 2012](A) P0 (B) 100 P0

(C) 400 P0 (D) 4 P0

53. Light of wavelength ph falls on a cathode plate

inside a vacuum tube as shown in the figure. The

work function of the cathode surface is and the

anode is a wire mesh of conducting material kept at

a distance d from the cathode. A potential difference

V is maintained between the electrodes. If the

minimum de Broglie wavelength of the electrons

passing through the anode is e , which of the

following statement(s) (are) true [JEE 2016]

Light

Electrons

V+

(A) For large potential difference eV / e ,

is approximately halved if V is made four times(B) e increases at the same rate as ph for

ph hc /

(C) e is approximately halved, if d is doubled

(D) e decreases with increase in and ph

54. Which of the following figure represents the variation

of particle momentum and the associated de-Broglie

wavelength [AIIMS 1982]

(A)

p

(B)

p

(C)

p

(D)

p

55. A photoelectric material having work-function 0 is

illuminated with light of wavelength 0

hc.

The

fastest photoelectron has a de Broglie wavelength

d. A change in wavelength of the incident light by

results in a change d din . Then the ratio

d is proportional to [JEE 2017]

(A)3d2

(B)3d

(C)2d2

(D) d

56. The stopping potential V for photoelectric emission

from a metal surface is plotted along Y-axis and

frequency v of incident light along X-axis. A straight

line is obtained as shown. Planck’s constant is given

by

O

Y

X

V

v

(A) Slope of the line(B) Product of slope on the line and charge on the

electron(C) Product of intercept along Y-axis and mass of

the electron(D) Product of slope and mass of electron

57. Photoelectric effect experiments are performed usingthree different metal plates p, q and r having workfunctions

p q r2.0eV, 2.5eV and 3.0eV,

respectively. A light beam containing wavelengths of550 nm, 450 nm and 350 nm with equal intensitiesilluminates each of the plates. The correct I-V graphfor the experiment is. (Take hc = 1240 eV nm]

(A)

I

V

rqp

(B)

I

Vrqp

(C)

I

V

rqp (D)

I

V

r q p

58. For photo-electric effect with incident photowavelength , the stopping potential is V0. Identifythe correct variation(s) of V0 with and 1 /

[JEE 2015]

(A)

V0

(B)

V0

(C)

1/

(D)

V0

59. The graph between 1 / and stopping potential (V)

of three metals having work functions 1 2 3, and in an experiment of photo- electric effect is plottedas shown in the figure. Which of the followingstatement is correct [Here is the wavelength ofthe incident ray] [JEE 2006]

Que. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Ans. B D C C D D D C B A B C C B A

Que. 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Ans. B A C B B B C C A B A D C B A

Que. 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

Ans. D D C D D A C A AB D D A C C B

Que. 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Ans. C AB A D D B C A D A B A AC AC BC

EXERCISE - II ANSWER KEY

Que. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Ans. B D A B D C A A B D B B D C C

Que. 16 17 18 19 20 21 22 23 24 25

Ans. A B D ABC D B ACD A D B

EXERCISE - I ANSWER KEY

0.001 0.002 0.004 1/ nm-1

Vmetal 1 metal 2 metal 3

(A) Ratio of work functions 1 2 3: : 1 : 2 : 4

(B) Ratio of work functions 1 2 3: : 4 : 2 : 1

(C) tan is directly proportional to hc/e, where his Planck’s constant and c is the speed of light

(D) The violet colour light can eject photoelectronsfrom metals 2 and 3

60. The de-Broglie wavelength of a photon is twice, thede-Broglie wavelength of an electron. The speed of

the electron is e

cv

100 . Then,

(A)4e

p

E10

E (B)

2e

p

E10

E

(C)2e

e

p10

m c (D)

4e

e

p10

m c