Electromagnetic Waves | Physics JEE Main questions with Solutions

Q 1 :
An alternating voltage of amplitude 40 V and frequency 4 kHz is applied directly across the capacitor of 12 $μ F$ . The maximum displacement current between the plates of the capacitor is nearly [2024]

12 A
13 A
10 A
8 A

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(A) Displacement current is same as conduction current in capacitor.

$X_{C} = \frac{1}{ω C} = \frac{1}{2 π f C}$

$= \frac{1}{2 π \times 4 \times 10^{3} \times 12 \times 10^{- 6}} = 3.317 Ω$

$I = \frac{V}{X_{C}} = \frac{40}{3.317} = 12 A$

Q 2 :
Electromagnetic waves travel in a medium with speed of $1.5 \times 10^{8}$ $m s^{- 1}$ . The relative permeability of the medium is 2.0. The relative permittivity will be: [2024]

2
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(A) $Speed of light in vacuum = \frac{1}{\sqrt{μ_{0} ϵ_{0}}} = 3 \times 10^{8}$

$Speed of light in medium = \frac{1}{\sqrt{μ_{0} \in_{0}} \cdot \sqrt{μ_{r} \in_{r}}} = \frac{3}{2} \times 10^{8}$

$Also, given, ϵ_{r} = 2, therefore, μ_{r} = 2$

Q 3 :
A plane EM wave is propagating along $x$ direction. It has a wavelength of 4 mm. If electric field is in $y$ direction with the maximum magnitude of 6O $V m^{- 1}$ , the equation for magnetic field is [2024]

$B_{z} = 60 \sin [\frac{π}{2} (x - 3 \times 10^{8} t)] \hat{k} T$
$B_{z} = 2 \times 10^{- 7} \sin [\frac{π}{2} \times 10^{3} (x - 3 \times 10^{8} t)] \hat{k} T$
$B_{x} = 60 \sin [\frac{π}{2} (x - 3 \times 10^{8} t)] \hat{i} T$
$B_{z} = 2 \times 10^{- 7} \sin [\frac{π}{2} (x - 3 \times 10^{8} t)] \hat{k} T$

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(B) $λ = 4 m m = 4 \times 10^{- 3} m$

$K = \frac{2 π}{4 \times 10^{- 3}} = \frac{π}{2} \times 10^{3} \cdot m^{- 1}$

$ω = v \times K = 3 \times 10^{8} \times \frac{π}{2} \times 10^{3} = \frac{3 π}{2} \times 10^{11} r a d / s$

Electric field $\Rightarrow y$ direction

Propagation field $\Rightarrow x$ direction

Mgnetic field $\Rightarrow z$ direction

$\hat{E} \times \hat{B} = \hat{c}$ and $B_{0} = \frac{E_{0}}{c} = 2 \times 10^{- 7} T$

$B_{z} = 2 \times 10^{- 7} \sin [\frac{π}{2} \times 10^{3} (x - 3 \times 10^{8} t)] \hat{k} T$

Q 4 :
The magnetic field in a plane electromagnetic wave is $B_{y} = (3.5 \times 10^{- 7}) \sin (1.5 \times 10^{3} x + 0.5 \times 10^{11} t) T .$ The corresponding electric field will be [2024]

$E_{y} = 1.17 \sin (1.5 \times 10^{3} x + 0.5 \times 10^{11} t) V m^{- 1}$
$E_{z} = 105 \sin (1.5 \times 10^{3} x + 0.5 \times 10^{11} t) V m^{- 1}$
$E_{z} = 1.17 \sin (1.5 \times 10^{3} x + 0.5 \times 10^{11} t) V m^{- 1}$
$E_{y} = 10.5 \sin (1.5 \times 10^{3} x + 0.5 \times 10^{11} t) V m^{- 1}$

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(B) $E_{0} = B_{0} c$

$E_{Z} = 3 \times 10^{8} \times (3.5 \times 10^{- 7}) \sin (1.5 \times 10^{3} x + 0.5 \times 10^{11} t)$

$E_{z} = 105 \sin (1.5 \times 10^{3} x + 0.5 \times 10^{11} t) V m^{- 1}$

Q 5 :
Match Column I with Column II

Column I Column II

A. $\oint \vec{B} \cdot d l = μ_{0} i_{c} + μ_{0} ϵ_{0} \frac{d Φ_{E}}{d t}$ I. Gauss' law for electricity

B. $\oint \vec{E} \cdot \vec{d} l = \frac{d Φ_{B}}{d t}$ II. Gauss' law for magnetism

C. $\oint \vec{E} \cdot \vec{d} A = \frac{Q}{ϵ_{0}}$ III. Faraday law

D. $\oint \vec{B} \cdot \vec{d} A = 0$ IV. Ampere-Maxwell law

Choose the correct answer from the options given below [2024]

A-IV, B-I, C-III, D-II
A-II, B-III, C-I, D-IV
A-IV, B-III, C-I, D-II
A-I, B-II, C-III, D-IV

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(C) Ampere-Maxwell law, $\oint \vec{B} \cdot d l = μ_{0} i_{c} + μ_{0} ϵ_{0} \frac{d Φ_{E}}{d t}$

Faraday law, $\oint \vec{E} \cdot \vec{d} l = \frac{d Φ_{B}}{d t}$

Gauss' law for electricity $\oint \vec{E} \cdot \vec{d} A = \frac{Q}{ϵ_{0}}$

Gauss' law for magnetism $\oint \vec{B} \cdot \vec{d} A = 0$

Q 6 :
A plane electromagnetic wave of frequency 35 MHz travels in free space along the X-direction. At a particular point (in space and time) $\vec{E} = 9.6 \hat{j} V / m$ . The value of magnetic field at this point is [2024]

$9.6 \hat{j} T$
$3.2 \times 10^{- 8} \hat{i} T$
$3.2 \times 10^{- 8} \hat{k} T$
$9.6 \times 10^{- 8} \hat{k} T$

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(C) $\frac{E}{B} = 3 \times 10^{8}$

$B = \frac{E}{3 \times 10^{8}} = \frac{9.6}{3 \times 10^{8}}$

$B = 3.2 \times 10^{- 8} T \hat{B}$

$= \hat{i} \times \hat{j} = \hat{k}$

So, $\vec{B} = 3.2 \times 10^{- 8} \hat{k} T$

Q 7 :
The electric field of an electromagnetic wave in free space is represented as $\vec{E} = E_{0} \cos (ω t - k z) \hat{i}$ .

The corresponding magnetic induction vector will be : [2024]

$\vec{B} = E_{0} c \cos (ω t - k z) \hat{j}$
$\vec{B} = \frac{E_{0}}{c} \cos (ω t - k z) \hat{j}$
$\vec{B} = E_{0} c \cos (ω t + k z) \hat{j}$
$\vec{B} = \frac{E_{0}}{c} \cos (ω t + k z) \hat{j}$

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(B) Given $\vec{E} = E_{0} \cos (ω t - k z) \hat{i}$

$E_{0} = B_{0} c, \Rightarrow (B_{0} = \frac{E_{0}}{c})$

Also $\vec{E}$ and $\vec{B}$ are in same phase.

Q 8 :
Match List I with List II

List I List II

A Gauss's Law of Magnetostatics I $\oint \vec{E} \cdot \vec{d} a = \frac{1}{ϵ_{0}} \int ρ d V$

B Faraday's law of electromagnetic induction II $\oint \vec{B} \cdot \vec{d} a = 0$

C Ampere's Law III $\oint \vec{E} \cdot \vec{d} l = \frac{d}{d t} \int \vec{B} \cdot \vec{d} a$

D Gauss's law of Electrostatics IV $\oint \vec{B} \cdot \vec{d} l = μ_{0} I$

Choose the correct answer from the options given below: [2024]

A-I, B-III, C-IV, D-II
A-III, B-IV, C-I, D-II
A-IV, B-II, C-III, D-I
A-II, B-III, C-IV, D-I

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(D) (A) Gauss of magnetostatics $\to \oint \vec{B} \cdot d \vec{a} = 0$ (II)

(B) Faraday's law $\to \int \vec{E} \cdot d \vec{t} = - \frac{d}{d t} \int \vec{B} \cdot d \vec{a}$ (III)

(C) Ampere's law $\to \oint \vec{B} \cdot \vec{d t} = μ_{0} I$ (IV)

(D) Gauss of electro $\to \oint \vec{E} \cdot d \vec{a} = \frac{1}{ϵ_{0}} \int ρ d V$ (I)

Q 9 :
Given below are two statements:

Statement I: Electromagnetic waves carry energy as they travel through space and this energy is equally shared by the electric and magnetic fields.

Statement II: When electromagnetic waves strike a surface, a pressure is exerted on the surface.

In the light of the above statements, choose the most appropriate answer from the options given below: [2024]

Statement I is incorrect but Statement II is correct
Both Statement I and Statement II are correct.
Both Statement I and Statement II are incorrect.
Statement I is correct but Statement II is incorrect.

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(B) $\frac{1}{2} ϵ_{0} E^{2} = \frac{B^{2}}{2 μ_{0}}$

Q 10 :
If frequency of electromagnetic wave is 60 MHz and it travels in air along z-direction, then the corresponding electric and magnetic field vectors will be mutually perpendicular to each other, and the wavelength of the wave (in m) is: [2024]

2.5
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(C) $S p e e d = W a v e l e n g t h \times F r e q u e n c y$

$\Rightarrow λ = \frac{C}{f} = \frac{3 \times 10^{8}}{60 \times 10^{6}} = 5 m$

Topic Question Set

Q 1 :
An alternating voltage of amplitude 40 V and frequency 4 kHz is applied directly across the capacitor of 12 $μ F$ . The maximum displacement current between the plates of the capacitor is nearly [2024]

Q 2 :
Electromagnetic waves travel in a medium with speed of $1.5 \times 10^{8}$ $m s^{- 1}$ . The relative permeability of the medium is 2.0. The relative permittivity will be: [2024]

Q 3 :
A plane EM wave is propagating along $x$ direction. It has a wavelength of 4 mm. If electric field is in $y$ direction with the maximum magnitude of 6O $V m^{- 1}$ , the equation for magnetic field is [2024]

Q 4 :
The magnetic field in a plane electromagnetic wave is $B_{y} = (3.5 \times 10^{- 7}) \sin (1.5 \times 10^{3} x + 0.5 \times 10^{11} t) T .$ The corresponding electric field will be [2024]

Q 6 :
A plane electromagnetic wave of frequency 35 MHz travels in free space along the X-direction. At a particular point (in space and time) $\vec{E} = 9.6 \hat{j} V / m$ . The value of magnetic field at this point is [2024]

Q 7 :
The electric field of an electromagnetic wave in free space is represented as $\vec{E} = E_{0} \cos (ω t - k z) \hat{i}$ .

The corresponding magnetic induction vector will be : [2024]

Q 10 :
If frequency of electromagnetic wave is 60 MHz and it travels in air along z-direction, then the corresponding electric and magnetic field vectors will be mutually perpendicular to each other, and the wavelength of the wave (in m) is: [2024]

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	Column I		Column II
A.	$\oint \vec{B} \cdot d l = μ_{0} i_{c} + μ_{0} ϵ_{0} \frac{d Φ_{E}}{d t}$	I.	Gauss' law for electricity
B.	$\oint \vec{E} \cdot \vec{d} l = \frac{d Φ_{B}}{d t}$	II.	Gauss' law for magnetism
C.	$\oint \vec{E} \cdot \vec{d} A = \frac{Q}{ϵ_{0}}$	III.	Faraday law
D.	$\oint \vec{B} \cdot \vec{d} A = 0$	IV.	Ampere-Maxwell law

	List I		List II
A	Gauss's Law of Magnetostatics	I	$\oint \vec{E} \cdot \vec{d} a = \frac{1}{ϵ_{0}} \int ρ d V$
B	Faraday's law of electromagnetic induction	II	$\oint \vec{B} \cdot \vec{d} a = 0$
C	Ampere's Law	III	$\oint \vec{E} \cdot \vec{d} l = \frac{d}{d t} \int \vec{B} \cdot \vec{d} a$
D	Gauss's law of Electrostatics	IV	$\oint \vec{B} \cdot \vec{d} l = μ_{0} I$

Topic Question Set

Q 1 : An alternating voltage of amplitude 40 V and frequency 4 kHz is applied directly across the capacitor of 12 μF. The maximum displacement current between the plates of the capacitor is nearly [2024]

Q 2 : Electromagnetic waves travel in a medium with speed of 1.5×108 ms-1. The relative permeability of the medium is 2.0. The relative permittivity will be: [2024]

Q 3 : A plane EM wave is propagating along x direction. It has a wavelength of 4 mm. If electric field is in y direction with the maximum magnitude of 6O Vm-1, the equation for magnetic field is [2024]

Q 4 : The magnetic field in a plane electromagnetic wave is By=(3.5×10-7)sin(1.5×103x+0.5×1011t)T. The corresponding electric field will be [2024]

Q 6 : A plane electromagnetic wave of frequency 35 MHz travels in free space along the X-direction. At a particular point (in space and time) E→=9.6j^V/m. The value of magnetic field at this point is [2024]

Q 7 : The electric field of an electromagnetic wave in free space is represented as E→=E0cos(ωt-kz)i^. The corresponding magnetic induction vector will be : [2024]

Q 10 : If frequency of electromagnetic wave is 60 MHz and it travels in air along z-direction, then the corresponding electric and magnetic field vectors will be mutually perpendicular to each other, and the wavelength of the wave (in m) is: [2024]

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Q 1 :
An alternating voltage of amplitude 40 V and frequency 4 kHz is applied directly across the capacitor of 12 $μ F$ . The maximum displacement current between the plates of the capacitor is nearly [2024]

Q 2 :
Electromagnetic waves travel in a medium with speed of $1.5 \times 10^{8}$ $m s^{- 1}$ . The relative permeability of the medium is 2.0. The relative permittivity will be: [2024]

Q 3 :
A plane EM wave is propagating along $x$ direction. It has a wavelength of 4 mm. If electric field is in $y$ direction with the maximum magnitude of 6O $V m^{- 1}$ , the equation for magnetic field is [2024]

Q 4 :
The magnetic field in a plane electromagnetic wave is $B_{y} = (3.5 \times 10^{- 7}) \sin (1.5 \times 10^{3} x + 0.5 \times 10^{11} t) T .$ The corresponding electric field will be [2024]

Q 6 :
A plane electromagnetic wave of frequency 35 MHz travels in free space along the X-direction. At a particular point (in space and time) $\vec{E} = 9.6 \hat{j} V / m$ . The value of magnetic field at this point is [2024]

Q 7 :
The electric field of an electromagnetic wave in free space is represented as $\vec{E} = E_{0} \cos (ω t - k z) \hat{i}$ .

The corresponding magnetic induction vector will be : [2024]

Q 10 :
If frequency of electromagnetic wave is 60 MHz and it travels in air along z-direction, then the corresponding electric and magnetic field vectors will be mutually perpendicular to each other, and the wavelength of the wave (in m) is: [2024]