JEE NEET Physics Question Bank - Electro Magnetic Waves

15 Electro Magnetic Waves

  Q
Gauss's Law for electricity, vÔ E <d a G
close surface
H0

 
Gauss's law for magnetism, vÔ B <d a 0
close surface

The magnetic force line always form closed loops.

Faraday's Law :

dI d Ë  Û
emf H =  = Ì vÔ B < d a Ü
dt dt ÌÍ surface ÜÝ

The varying magnetic field generate electric field.

 
Ampere's circuital Law : vÔ B < d l N0 I
line

³ J <da
o o § o o·
¨' I J < d a¸
= P
surface © ¹

Ampere Maxwell Law :

o
vvÔ³ B < d l P0 Ic  P0 H0 ³
o o dE o
<da
dt

P0 I c  P0 I d

' P0 I P0 I c  I d

Ampere - Maxwell law shows that the total current passing through any surface of which the
closed loop is the perimeter is the sum of the, conduction current and the displacement current.
Where I c conduction current, I d displacement current, I = total current

Displacement current I d Ñ
Displacement current produced due to change of electric field or electric flux with time during
the procedure of charging or discharging of capacitor.
l When electric flux linked between two plates of capacitor become constant then displacement
current become zero.
l Displacement current and conduction current are equal during charging or discharging of capacitor.

402

l Magnetic field produced by displacement current like conduction current.

l Unit of displacement current and conduction current is same and is same as ‘A’ (Ampere)

³J <d a
o o
conduction current I c

dI E o o
Displacement current I d $ , where IE
dE
o o A<E
dt dt

Displacement current in integnal form.

o
o ³
dE o
Id <da
dt

Where permittivity of free space and Rate of change of electric field.
dE
o
dt

Hert'z Experiment
G
Induction coil Q1 V E
e

G
M E
G
Spark gap (S)
b
G
a

C D

N o
X Shows that B is perpendicular
Q2 Ve to the page directed into the page
at C and D
The produced electromagnetic waves travelling along the X direction shown in fig.
The spheres Q1, and Q2 constitute a capacitor while the rods behave as an inductor. Such an
arrangement can be considered equivalent to L-C oscillator circuit and known as Hertzian
Dipole. Dipole moment of it is p p 0 cos t

l The frequency of the generated electromagnetic waves is equal to the frequency of oscillation of the
electric changes.
l The energy of the electromagnetic waves is equal to the kinetic energy of the charges oscillating
between the two spheres.
l The electric field and magnetic field vectors oscillate in mutually perpendicular planes,
perpendicular to the direction of propogation of the waves.
o o
l The direction of propagation is that of E × B , it's magnitude (in free space) is 3 u 108 ms 1 .

403

(1) The direction of electric field and magnetic field are shown in figure (1) and (2) for a plane
electromagnetic wave travelling along X - direction. true option is ......
Y o Y
E o
B

o
C X
X
o o
fig. 2 C E fig. 1
o Z
Z B
(A) (1) right (2) wrong (B) (1) and (2) both right
(C) (2) right (1) wrong (D) (1) and (2) both wrong
(2) The electric field in Y direction and magnetic field in Z direction for an electromagnetic wave
passes in through the space. Which will be true option ?

§o o· o §o o· o §o o· o
(A) ¨ E u B ¸ < E (B) ¨ E u B ¸ < B 1 (C) ¨ E u B ¸ < B (D) None of above
© ¹ © ¹ © ¹
1 0

(3) The Hertzian dipole is shown in figure at time t. Which will be the Q1
o o
correct option given below for direction of E and B at point P.

P

Q2
(A) (B)
o
o E
B

o o
P P
E B

(C) (D)

o o
E E

o
B
P
P o
B

404

(4) The oscillation of charges of electric dipole shown in figure at time t which one is correct figure
of electric field lines and magnetic field line produce due to charges oscillation ?
(A) + (B) + (C) + (D) +

– – – –
(5) A sphere of mass 5 mg, having charge is hanged at one end of spring of force constant
Nm . (Shown in figure.) The frequency of emmited radiation will be
5 1 .
2 u 10
Rigid support
(A) (B) 2S Hz
1
Hz
2S

k (C) S Hz (D)
1
Hz
S

q
(6) For Hertzian dipole moment p po cos t which curve is true from given below, at time

and T.
T T 3T
t , ,
4 2 4

(A) po (B) po

O t O t

(C) P (D)
po po

O t O t

(7) From which is wrong characteristics of electromagnetic waves ?
(A) The maximum and minimum magnitude of electric field and magnetic field vectors produce at
same time and same point.
(B) The energy of electromagnetic wave is divide eqully in electric field and magnetic field.
(C) The electric field and magnetic field vectors oscillate in mutually perpendicular and also
perpendicular to the direction of propagation of the wave.
(D) Medium is not required for propagation of electromagnetic wave.
(8) Maxwell's equations indicated the fundamental basic of
(A) Only charge (B) Only magnet (C) Only mechanics (D) Both (A) and (B)

Ans. : 1 (A), 2 (C), 3 (C), 4 (B), 5 (D), 6 (A), 7 (C), 8 (D)

405

l Difference between Electromagnetic waves and Plane Electromagnetic Waves

Electromagnetic Wave Plane Electromagnetic Wave

o o
l The electric field ( E ) and magnetic field l The electric field E , and magnetic

o o
( B ) vector osccillate in mutually field B vector oscillate in mutually
perpendicular to each other and all perpendicular plane and perpendicular
possible perpendicular to propagation at propagation of direction along in
of direction. perticular direction
e.g. direction of propagnation in X- axis,
o
E vector in Y-axis
o
B vector in Z-axis

Here, 0 and
dE dE
0.
dx dr
l Unpolarized wave. l These waves are polarized wave.
l normally near to source area. l Normally far away from source.
l Cylindaric wave plate l Wave front are plane
l frequency is not constant l Constant frequency

Electric field Electric field
Wave length Magnetic
field Diraction
O = Wave length Magnetic of
Diraction of field Propoginationë
Propaginationë

l An Electromagnetic wave propagating along the X-direction
Y
G
E
direc
tion
G
of
G
prop
B
agat
E
O
ion
G

X Velocity c
B G
Z E G

l Characteristic of this waves
B

o o
l The equation of an electric field E and magnetic field B for electromagnetic wave.

406

o
Electric field E E x i  E y j  E z k but, E x 0, E z 0 and

E y = Eosin ( t  kx so,
o
E Eo sin t  kx j
Where angular frequency and k wave vector
o
Magnetic field B B x i  B y j  B z k but B x 0, B y 0 and

Bz Bo sin t  kx so,
o
B Bo sin t  kx k
l The velocity of electromagnetic wave in vaccum (free space) :
1
C
P0 R

P0 4S u 10 7 NA 2 permeability of free space.

o 8.85 u 10 12 C 2 N 1m 2 permittivity of free space.
l The vector of the electromagnetic waves perpendiculer through away medium :
1 1 c
v
P
or v P 0 P r o r or
v
Pr K .
Where P = permeability of medium
permittivity of medium
P
Pr relative permittivity of medium
P0

r Relative permeativity of medium
0

= K = Dielectric constant of the medium
l The refractive index of the medium :
c
n P1 K Pr r
v
o o
l Relation between E and B :
E cB
l If electromagnetic wave propagating along positive X direction then E y cBz and its

propagating along negative X-direction, Then E y  cB z .

§o o·
Direction of vector C = Direction of ¨ E u B ¸
o
l
© ¹

o o o c o
l E  c c u B and B c
uE

o o
Where c c unit vector of c . It's magnitude is 3.0 u 108 ms 1

407

l The electromagnetic energy per unit volume (energy density) of electromagnetic waves :

Energy density associated with electric field, UH ( 2 rms
1
l o
2
2
B rms
l Energy density associated with magnetic field U B 2P0

l Energy density associated with electromagnetic wave.
2
B rms
( rms or U
2
U o P0

l Intensity of electromagnetic wave :
Energy Power
Intensity I Time u Area Area

H 0 E02c
I 0
( 2 rms ˜ c Uc
2

Maximum intensity I max E o Bo

l Equation of intensity in form of B rms :
2
cB rms
I
P0

E rms ˜ Brms
I
P0

l Linear momentum by electromagnetic waves on surface :
U
P
c
Where U = The energy of electromagnetic waves incident on a surface and it is completly absorbed.
c = velocity of wave.
If incident energy totally reflect by surface then linear momentum obtain to the

surface P , because change in momentum is P   P
2U
2P .
c
l Pointing Vector :
A power passes through unit area in direction of propagating of wave is called pointing

vector (S) .
o

o o o
? S EuH

P P r Po
Wave impedance : Z
E
l H r o

o o
Where E Vector of electric field, H magnetic intensity

408

Energy E
l Momentum of wave P = Velocity c

o
l Radiation of pressure P
S
c
l Electro magnetic spectrum :
UD\V ;UD\V , Ultraviolet, Visible, Infrared, Microwave, Short radio wave, long radio wave
frequency f decrease (from UD\V to radio wave) (value is in decreasing order)
Wave length increases (from J -rays to radio wave) (value is in ascending order)
l Wave length range, production, detection and uses of different types of electromagnetic waves.
Type Wavelength Production Detection Uses
Range
Radio > 0.1m Rapid acceleration and Receiver's Used in radio and TV commu-
decelerations of aerials (conduc- nication system
electrons in aerials ting wire)
Microwave 0.1m to Klystron magnetron, Point contact Maglev train, RADAR, air
1 mm Gun diode. diodes craft, navigation, interceptor
vans, ovens
Infrared 1 mm to Vibration of atoms and Thermopile Infrared lamps are used in
(IR) 700 nm molecules Bolometer, physiotheraphy, infrared
infrared detectors are used in remote
sensing satellites for milletary
purpose, agriculture, remote
control of TV, video players
and wifi systems.
Visible Light 700 nm to Electrons in atom, emit The eye, photo- Used for visibility of objects
400 nm light when they move cells, photogra-
from one energy level phic film, photo
to a lower energy level. diode,
light dependen-
tresistor (LDR)
Ultraviolet 400 nm to Inner shell electrons in Solar cell, Pho- Lasik eye surgery, water
1 nm molecule moving from tocells, photo- purifiers, UV lamps are used to
one energy level to a graphic film kill germs.
lower level.
X-ray 1 nm to X-ray tubes or inner Photographic Used in medical applications
10-3 nm shell electrons of film to find the fracture in bones,
molecule Geiger tubes, as well as in a treatment of
Ionization certain types of cancer.
chamber.
Gamma 3
 10 nm Radioactive decay of - do - Are used in medicine to
rays the nucleus destroy cancer cells

409

ª § x ·º
(9) The electric field of an electromagnetic wave is given by E 8.284 « 7.54 u 106 ¨¨ t  ¸ » mVm
8 ¸
1
«¬ © 3 u 10 ¹ »¼

The energy density field will be .
(A) 318.5 u 10 19 J (B) 318.5 u 1019 Wm3 (C) 318.5 u 1019 Jm 3 (D) 318.5 u 1019 W

(10) The electric field of an electromagnetic wave with intensity 1.328 Wm2 is given by

o
E E o sin ªS 9 u 1014 t  3 u 106 º i Then X component of electric field E x will be
¬ ¼

( c 3 u 108 ms 1 ), ( o  × 10 SI )
-2

(A) 100 (B) 10 10 (C) 0.1 (D) 1000

(11) The electric field of an electro magnetic wave is given by E 10 sin ª30 u 10 t  10 x º . Then
¬ ¼
14 7

radiation pressure will be .
(A) 4.42 u 10 8 Pa (B) 442 Pa (C) 4.42 u 1010 Pa (D) 442 × 1010 Pa

(12) Radiation pressure on earth's surface by sunlight of average intensity 1480 Wm2 is incident on

surface of earth is (take c 3 u 10 ms )
8 1

(A) 49.3 u 106 (B) 49.3 u 105 (C) 4.93 u 106 (D) 4.93 u 105

(13) The permeability of medium having refractive index 1.5 and dielectric is 2, will be

4S u 10
7 1
TmA1 . P0 TmA

(A) 0.45 S u 107 (B) 5S u 107 (C) 5S u 107 (D) 4.5S u 107

(14) An average intensity of electromagnetic energy is proportional to square of amplitude of wave. In
this statement the dimensional formula of proportional constant will be .

(A) M1 L2 T 3 A 1 (B) M 1 L2 T 3 A 2 (C) M1 L2 T 3 A 2 (D) M 1 L2 T 3 A1

(15) If 50 W radiation energy incident on one surface and it completely absorbed by surface then
magnitude of E rms and B rms will be Vm1 and T.

(A) 15. 5 u 108 (B) 21. 7 u 108 (C) 18. 6 u 108 (D) 27. 9 u 108

(16) The energy of an electro magnetic waves which are passes through a volume DV, associate with
this volume, then fregnency of this energy's oscillation is .
(A) zero (B) half the frequency of the wave
(C) the frequency of the wave (D) double the frequency of the wave

410

(17) The electric field in an em wave is given by E 50 sin ª Z t  x º . Then the energy contained
¬« c ¼»

in a cylinder of cross-section 20 mm2 and length 50 cm along the X-axis is J.

(A) 4.5 u 1012 (B) 7.5 u 1012 (C) 5 u 1012 (D) 5.5 u 1012

(18) The intensity of the sunlight on the earth is 1380 Wm -2 . Assume this light to be a plane

monochromatic wave. Then the amplitude of the magnetic field in the wave is T.

(A) 3.4 u 10 6 (B) 5 u 104 (C) 4.2 u 106 (D) 2.6 u 104

(19) An em-wave passing through vaccum is described by E E o sin kx  t . Which of the

following is indipendent of the wave length .

(A) (B) k (C) (D) k
k

(20) If magnetic monopole existed then which of the following Maxwell's equation would be
modified ?

   
(A) vÔ E ¹ d a
qm
(B) vÔ E ¹ d l d  
B ¹d a
H0 dt Ô

dt ³
d o o
( ˜ d a  P0i
 
(C) vÔ B ¹ d a 0 (D) P0 o

(21) A long straight wire of resistance R, radius a and length l carries a constant current I. The
pointing vector for the wire will be .

(A) 2ISRal (B) I R (C) IR (D) I R
2 2 2
al al 2 Sal

(22) Micro waves are used for communication and in RADAR because .
(A) They have short wave length (B) Its very less diffraction

(C) Its more diffraction (D) Its propagination with high speed

(23) Give the name of the devices which produced visible light.

(A) Klystrons (B) Magnetrons

(C) Gunn diodes (D) Incondencent lamp

Ans. : 9 (B), 10 (B), 11 (C), 12 (C), 13 (D), 14 (B), 15 (D), 16 (D), 17 (D), 18 (A),
19 (A), 20 (A), 21 (D), 22 (B), 23 (D)

411

Assertion - Reason type Question :

Instruction : Read assertion and reason carefully, select proper option from given below.

(a) Both assertion and reason are true and reason explains the assertion.

(b) Both assertion and reason are true but reason does not explain the assertion.

(c) Assertion is true but reason is false.

(d) Assertion is false and reason is true.
(24) Assertion : When an electromagnetic wave going through vaccum is described as
E E o sin kx  t , then Z is independent of the wavelength
k

Reason Ñ Zk is speed of the wave.
(A) a (B) b (C) c (D) d
(25) Assertion : Displacement current goes through the gap of a capacitor whenever the charge
of the capacitor increases or decreases.

dI E
Reason Ñ Displacement current I d P0
dt
(A) a (B) b (C) c (D) d
(26) Assertion : The energy contained in a small volume through which an em wave is passing
oscillates with the frequency of the wave.

Reason Ñ Energy density of the wave is given by
1
o
E2
2
(A) a (B) b (C) c (D) d
Ans. : 24 (a), 25 (a), 26 (D)

Comprehension Type Questions :
Passage-I :
A light beam travelling in the X-direction is described by the electric field
§ x·
300 sin ¨ Z t  ¸ Vm 1 . An electron is allowed to move along the Y-direction with a speed of
© c¹
Ey

2 u 10 7 ms 1 .

(27) The maximum magnetic field is .

(A) 9 u 1010 T  Z direction (B) 9 u 1010 T  Z direction

(C) 10 6 T  Z direction (D) 10 6 T  Z direction

(28) The maximum electric force on the electron is N.

(A) 4.8 u 1017 (B) 3.6 u 1017 (C) 2.4 u 1017 (D) 1.2 u 1017

412

(29) The maximum magnetic force on the electron is N.

(A) 4.8 u 1018 (B) 3.2 u 1018 (C) 6.4 u 1018 (D) 1.6 u 1018

Passage-II :

ª 1 §  x ·º
200 sin « 4 u 10 S ¨t ¸ PT
c ¹ »¼
The magnetic field in a plane em wave is given by B
©
15

¬

If c 3 u 10 ms , then answer the following questions :
8 1

(30) The maximum electrical field is NC .
–1

(A) 2 u 10 4 (B) 6 u 104 (C) 5 u 104 (D) 3 u 104

(31) The average energy is Jm .
3

(A) 18 u 103 (B) 21 u 103 (C) 24 u 103 (D) 16 u 103

(32) Magnitude of pointing vector of electromagnetic wave is A T –1 s –1 .

(A) 9.55 u 106 (B) 3.17 u 106 (C) 4.75 u 106 (D) 6.34 u 106

Passage-III :
A 2000 W bulb is kept at the centre of a spherical surface at a distance of 20 m from the surface.
The working efficiencey of the bulb is 2 % and consider it as point source. Give answer the following
question :

Ho 8.85 u 10 SI and c
12
3 u 108 ms 1

(33) Maximum magnitude of electric field E o for electromagnetic wave is .

(A) 1.73 NC-1 (B) 2.45 NC-1 (C) 7.96 NC-1 (D) 7.13 NC-1

(34) Intensity of electromagnetic wave is Wm
2 .

(A) 1.73 u 103 (B) 2.45 u 103 (C) 7.96 u 103 (D) 7.13 u 103

(35) Force acting on surface N.

(A) 7.5 u 10 8 (B) 1.33 u 107 (C) 2.65 u 107 (D) 2.45 u 107

(36) Density on surface Jm
3 .

(A) 1.33 u 1010 (B) 2.65 u 1011 (C) 7.50 u 108 (D) 2.65 u 1010

Ans. : 27 (C), 28 (A), 29 (B), 30 (B), 31 (D), 32 (A), 33 (B), 34 (C), 35 (B), 36 (B)

ˆ

413