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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(1)

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
1
5
4

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(1)

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

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

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

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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(2)

$λ = 4 m m = 4 \times 10^{- 3} m$

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

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

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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(2)

$E_{0} = B_{0} c$

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

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

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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(3)

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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(3)

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

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

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

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

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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(2)

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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(4)

(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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(2)

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

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
10
5
2

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(3)

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

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

Q 11 :

A parallel plate capacitor has a capacitance $C = 200$ $p F$ . It is connected to 230 V AC supply with an angular frequency 300 rad/s. The RMS value of conduction current in the circuit and displacement current in the capacitor respectively are [2024]

$1.38 μ A$ and $1.38 μ A$
$14.3 μ A$ and $143 μ A$
$13.8 μ A$ and $138 μ A$
$13.8 μ A$ and $13.8 μ A$

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(4)

Q 12 :

The electric field in an electromagnetic wave is given by $\vec{E} = \hat{i} 40 \cos ω (t - \frac{z}{c}) {NC}^{- 1}$ . The magnetic field induction of this wave is (in SI unit): [2024]

$\vec{B} = \hat{j} 40 \cos ω (t - \frac{z}{c})$
$\vec{B} = \hat{k} \frac{40}{c} \cos ω (t - \frac{z}{c})$
$\vec{B} = \hat{i} \frac{40}{c} \cos ω (t - \frac{z}{c})$
$\vec{B} = \hat{j} \frac{40}{c} \cos ω (t - \frac{z}{c})$

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(4)

$\vec{E} = 40 \cos (ω t - \frac{ω}{c} z) {NC}^{- 1} \hat{i}$

$\vec{E}$ is along $+ x$ direction

$\vec{v}$ is along $+ z$ direction

and Direction of $\hat{c}$ must be along $\vec{E} \times \vec{B}$ .

So direction of $\vec{B}$ will be along $+ y$ and magnitude of $\vec{B}$ will be $\frac{E_{0}}{c} .$

$B_{0} = \frac{E_{0}}{c} = \frac{40}{c}$

Q 13 :

The electric field of an electromagnetic wave in free space is

$\vec{E} = 57 \cos [7.5 \times 10^{6} t - 5 \times 10^{- 3} (3 x + 4 y)] (4 \hat{i} - 3 \hat{j}) N / C$

The associated magnetic field in Tesla is: [2025]

$\vec{B} = \frac{57}{3 \times 10^{8}} \cos [7.5 \times 10^{6} t - 5 \times 10^{- 3} (3 x + 4 y)] (5 \hat{k})$
$\vec{B} = \frac{57}{3 \times 10^{8}} \cos [7.5 \times 10^{6} t - 5 \times 10^{- 3} (3 x + 4 y)] (\hat{k})$
$\vec{B} = - \frac{57}{3 \times 10^{8}} \cos [7.5 \times 10^{6} t - 5 \times 10^{- 3} (3 x + 4 y)] (5 \hat{k})$
$\vec{B} = - \frac{57}{3 \times 10^{8}} \cos [7.5 \times 10^{6} t - 5 \times 10^{- 3} (3 x + 4 y)] (\hat{k})$

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(3)

E = CB

B = $\frac{57 \times 5}{3 \times 10^{8}}$

$3 \hat{i} + 4 \hat{j}$ is direction of propagation

$\Rightarrow (4 \hat{i} - 3 \hat{j}) \times (- \hat{k}) = 4 \hat{j} + 3 \hat{i}$

Q 14 :

A plane electromagnetic wave of frequency 20 MHz travels in free space along the +x direction. At a particular point in space and time, the electric field vector of the wave is $E_{y} = 9.3 {Vm}^{- 1}$ . Then, the magnetic field vector of the wave at the point is [2025]

$B_{z} = 9.3 \times 10^{- 8} T$
$B_{z} = 1.55 \times 10^{- 8} T$
$B_{z} = 6.2 \times 10^{- 8} T$
$B_{z} = 3.1 \times 10^{- 8} T$

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(4)

E = BC

$9.3 = B \times 3 \times 10^{8}$

$B = \frac{9.3}{3 \times 10^{8}} = 3.1 \times 10^{- 8} T$

Q 15 :

The magnetic field of an E.M. wave is given by

$\vec{B} = (\frac{\sqrt{3}}{2} \hat{i} + \frac{1}{2} \hat{j}) 30 \sin [ω (t - \frac{z}{c})]$ (SI Units)

The corresponding electric field in S.I. units is: [2025]

$\vec{E} = (\frac{1}{2} \hat{i} - \frac{\sqrt{3}}{2} \hat{j}) 30 c \sin [ω (t - \frac{z}{c})]$
$\vec{E} = (\frac{3}{4} \hat{i} + \frac{1}{4} \hat{j}) 30 c \cos [ω (t - \frac{z}{c})]$
$\vec{E} = (\frac{1}{2} \hat{i} + \frac{\sqrt{3}}{2} \hat{j}) 30 c \sin [ω (t + \frac{z}{c})]$
$\vec{E} = (\frac{\sqrt{3}}{2} \hat{i} - \frac{1}{2} \hat{j}) 30 c \sin [ω (t + \frac{z}{c})]$

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$\vec{B} = (\frac{\sqrt{3}}{2} \hat{i} + \frac{1}{2} \hat{j}) 30 \sin [ω (t - \frac{z}{c})]$

$\vec{E} \times \vec{B} = \vec{c} and E_{0} = B_{0} c$

Here $E = (\frac{\sqrt{3}}{2} (- \hat{j}) + \frac{1}{2} \hat{i})$

$E_{0} = 30 c$

$\vec{E} = (\frac{1}{2} \hat{i} - \frac{\sqrt{3}}{2} \hat{j}) 30 c \sin [ω (t - \frac{z}{c})]$

Q 16 :

A plane electromagnetic wave propagates along the +x direction in free space. The components of the electric field, $\vec{E}$ and magnetic field, $\vec{B}$ vectors associated with the wave in Cartesian frame are: [2025]

$E_{y}, B_{x}$
$E_{y}, B_{z}$
$E_{x}, B_{y}$
$E_{z}, B_{y}$

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(2)

Direction of wave propogation $\to \vec{E} \times \vec{B}$

Q 17 :

If $ε_{0}$ denotes the permittivity of free space and $Φ_{E}$ is the flux of the electric field through the area bounded by the closed surface, then dimension of $(ε_{0} \frac{d ϕ_{E}}{d t})$ are that of: [2025]

Electric field
Electric potential
Electric charge
Electric current

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(4)

We know that formula for displacement current is given by

$i_{d} = ε_{0} \frac{d ϕ_{ε}}{d t}$

Dimension of $ε_{0} (\frac{d ϕ_{E}}{d t})$ will be

Same as electric current

So $[ε_{0} \frac{d ϕ_{E}}{d t}] = A$

Q 18 :

A parallel plate capacitor of area A = 16 ${cm}^{2}$ and separation between the plates 10 cm, is charged by a DC current. Consider a hypothetical plane surface of area $A_{0} = 3.2 {cm}^{2}$ inside the capacitor and parallel to the plates. At an instant, the current through the circuit is 6 A. At the same instant the displacement current through $A_{0}$ is _______ mA. [2025]

(1200)

$i_{d} = i_{c}$

$∴$ Total displacement current = 6 A

Current density, $J_{d} = \frac{I}{A} = \frac{6}{16}$

$∴$ The current through small area $i' = J_{d} \times A'$

$i' = \frac{6}{16} \times 3.2 = 1.12 A = 1200 mA$

Q 19 :

A time varying potential difference is applied between the plates of a parallel plate capacitor of capacitance 2.5 $μ$ F. The dielectric constant of the medium between the capacitor plates is 1. It produces an instantaneous displacement current of 0.25 mA in the intervening space between the capacitor plates, the magnitude of the rate of change of the potential difference will be _______ ${Vs}^{- 1}$ .

(100)

q = CV

Differentiating, $i = \frac{C d V}{d t}$

$\Rightarrow \frac{d V}{d t} = \frac{0.25 \times 10^{- 3}}{2.5 \times 10^{- 6}} = \frac{1000}{10} = 100$

Q 20 :

Match List I with List II: [2023]

List I List II

A. Gauss’s Law in Electrostatics I. $\oint \vec{E} \cdot d \vec{l} = - \frac{d ϕ_{B}}{d t}$

B. Faraday’s Law II. $\oint \vec{B} \cdot d \vec{A} = 0$

C. Gauss’s Law in Magnetism III. $\oint \vec{B} \cdot d \vec{l} = μ_{0} i_{c} + μ_{0} ε_{0} \frac{d ϕ_{E}}{d t}$

D. Ampere-Maxwell Law IV. $\oint \vec{E} \cdot d \vec{S} = \frac{q}{ε_{0}}$

Choose the correct answer from the options given below:

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

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(2)

Gauss's law of electrostatics

$ϕ = \oint \vec{E} \cdot d \vec{s} = \frac{q}{ε_{0}}$

Faraday's law $\oint \vec{E} \cdot d \vec{l} = \frac{- d ϕ_{B}}{d t}$

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

Ampere's Maxwell law

$\oint \vec{B} \cdot d \vec{l} = μ_{0} i_{C} + μ_{0} ε_{0} \frac{d ϕ_{E}}{d t}$

Where $i_{C}$ : Conduction current

$ε_{0} \frac{d ϕ_{E}}{d t}$ : Displacement current

Q 21 :

A plane electromagnetic wave of frequency 20 MHz propagates in free space along $x$ -direction. At a particular space and time, $\vec{E} = 6.6 \hat{j} V/m$ . What is $\vec{B}$ at this point? [2023]

$- 2.2 \times 10^{- 8} \hat{i} T$
$2.2 \times 10^{- 8} \hat{k} T$
$- 2.2 \times 10^{- 8} \hat{k} T$
$2.2 \times 10^{- 8} \hat{i} T$

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(2)

$\hat{E} = 6.6 \hat{j}, ν = 20 MHz, \vec{c} = 3 \times 10^{8} \hat{i}$

$| \vec{B} |$ $= \frac{| \vec{E} |}{c} = 2.2 \times 10^{- 8} T$

$\hat{E} \times \hat{B} = \hat{c} \Rightarrow \hat{B} = 2.2 \times 10^{- 8} \hat{k} T$

Q 22 :

Which of the following Maxwell’s equations is valid for time varying conditions but not valid for static conditions? [2023]

$\oint \vec{B} \cdot \vec{d l} = μ_{0} I$
$\oint \vec{E} \cdot \vec{d l} = 0$
$\oint \vec{E} \cdot \vec{d l} = - \frac{\partial ϕ_{B}}{\partial t}$
$\oint \vec{D} \cdot \vec{d A} = Q$

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(3)

Based on equations of Maxwell

Q 23 :

The source of time varying magnetic field may be [2023]

(A) a permanent magnet
(B) an electric field changing linearly with time
(C) direct current
(D) a decelerating charge particle
(E) an antenna fed with a digital signal

Choose the correct answer from the options given below:

(D) only
(C) and (E) only
(A) only
(B) and (D) only

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(1)

Source of time varying magnetic field may be

→ accelerated or retarded charge which produces varying electric and magnetic fields.

→ An electric field varying linearly with time will not produce variable magnetic field as current will be constant

Q 24 :

In an electromagnetic wave, at an instant and at a particular position, the electric field is along the negative $z$ -axis and magnetic field is along the positive $x$ -axis. Then the direction of propagation of electromagnetic wave is [2023]

at 45° angle from positive y-axis
negative y-axis
positive z-axis
positive y-axis

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(2)

Direction of propagation of EM wave will be in the direction of $\vec{E} \times \vec{B}$ .

Q 25 :

To radiate EM signal of wavelength $λ$ with high efficiency, the antennas should have a minimum size equal to [2023]

$\frac{λ}{2}$
$\frac{λ}{4}$
$2 λ$
$λ$

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(2)

Minimum length of antenna should be $\frac{λ}{4}$ .

Q 26 :

In a medium the speed of light wave decreases to 0.2 times to its speed in free space. The ratio of relative permittivity to the refractive index of the medium is $x : 1$ . The value of $x$ is _______. (Given speed of light in free space $= 3 \times 10^{8} {ms}^{- 1}$ and for the given medium $μ_{r} = 1$ ) [2023]

(5)

$v = \frac{C}{μ} \Rightarrow μ = \frac{C}{v} = \frac{C}{0.2 C} = 5$

$μ = \sqrt{ε_{r} μ_{r}} \Rightarrow ε_{r} = \frac{μ^{2}}{μ_{r}}$

$\frac{ε_{r}}{μ} = \frac{μ}{μ_{r}} = 5$

Q 27 :

Match List – I with List – II. [2026]

List – I List – II

(Relation) (Law)

A. $\oint \vec{E} \cdot d \vec{l} = - \frac{d}{d t} \oint \vec{B} \cdot \vec{d a}$ I. Ampere’s circuital law

B. $\oint \vec{B} \cdot \vec{d l} = μ_{0} (I + ε_{0} \frac{d Φ_{E}}{d t})$ II. Faraday’s laws of electromagnetic induction

C. $\oint \vec{E} \cdot \vec{d a} = \frac{1}{ε_{0}} \int_{V} ρ d V$ III. Ampere–Maxwell law

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

Choose the correct answer from the options given below:

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

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(2)

Theoretical

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

Q 28 :

The electric field in a plane electromagnetic wave is given by :

$E_{y} = 69 \sin [0.6 \times 10^{3} x - 1.8 \times 10^{11} t] V / m$

The expression for magnetic field associated with this electromagnetic wave is ________ T. [2026]

$B_{z} = 2.3 \times 10^{- 7} \sin [0.6 \times 10^{3} x + 1.8 \times 10^{11} t]$
$B_{z} = 2.3 \times 10^{- 7} \sin [0.6 \times 10^{3} x - 1.8 \times 10^{11} t]$
$B_{y} = 69 \sin [0.6 \times 10^{3} x + 1.8 \times 10^{11} t]$
$B_{y} = 2.3 \times 10^{- 7} \sin [0.6 \times 10^{3} x - 1.8 \times 10^{11} t]$

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(2)

$\hat{B} = \hat{c} \times \hat{E}$

$\Rightarrow \hat{c} = \hat{i} because phase of electric field is function of x .$

$\Rightarrow \hat{E} = \hat{j} (given)$

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

$| B |$ $= \frac{| E |}{c} = \frac{69 \times 0.6 \times 10^{3}}{1.8 \times 10^{11}} = \frac{69}{3 \times 10^{8}}$

$| B |$ $= 2.9 \times 10^{- 7}$

$\vec{B_{2}} = 2.9 \times 10^{- 7} \sin (0.6 \times 10^{3} x - 1.8 \times 10^{11} t)$

(phase is same as that of electric field)

Q 29 :

The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by

$E_{y} = 20 \sin (3 \times 10^{6} x - 4.5 \times 10^{14} t) V/m,$

(where $x$ , $t$ and other values have S.I. units). The dielectric constant of the medium is __________.

(Speed of light in free space $3 \times 10^{8}$ m/s) [2026]

(4)

$n = \frac{C}{V}$

$V = \frac{ω}{k} = \frac{4.5 \times 10^{14}}{3 \times 10^{6}} = \frac{3}{2} \times 10^{8}$

$n = 2$

$n = \sqrt{μ_{r} ε_{r}} (μ_{r} = 1)$

$2 = \sqrt{ε_{r}}$

$ε_{r} = 4$

Q 30 :

A plane electromagnetic wave is moving in free space with velocity $c = 3 \times 10^{8} m/s$ and its electric field is given as $\vec{E} = 54 \sin (k z - ω t) \hat{j} V/m,$ where $\hat{j}$ is the unit vector along y-axis. The magnetic field vector $\vec{B}$ of the wave is: [2026]

$- 1.8 \times 10^{- 7} \sin (k z - ω t) \hat{i} T$
$1.4 \times 10^{- 7} \sin (k z - ω t) \hat{i} T$
$1.4 \times 10^{- 7} \sin (k z - ω t) \hat{k} T$
$+ 1.8 \times 10^{- 7} \sin (k z - ω t) \hat{i} T$

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(1)

$\hat{B} = \hat{C} \times \hat{E} = \hat{k} \times \hat{j} = - \hat{i}$

$∴$ $\vec{B} = \frac{54}{3 \times 10^{8}} \sin (k z - ω t) (- \hat{i})$

$= - 1.8 \times 10^{- 7} \sin (k z - ω t) \hat{i}$

Topic Question Set

Q 1 :

An alternating voltage of amplitude 40 V and frequency 4 kHz is applied directly across the capacitor of 12 $μ F$ . 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]

Q 11 :

A parallel plate capacitor has a capacitance $C = 200$ $p F$ . It is connected to 230 V AC supply with an angular frequency 300 rad/s. The RMS value of conduction current in the circuit and displacement current in the capacitor respectively are [2024]

(4)

Q 12 :

The electric field in an electromagnetic wave is given by $\vec{E} = \hat{i} 40 \cos ω (t - \frac{z}{c}) {NC}^{- 1}$ . The magnetic field induction of this wave is (in SI unit): [2024]

Q 13 :

The electric field of an electromagnetic wave in free space is

$\vec{E} = 57 \cos [7.5 \times 10^{6} t - 5 \times 10^{- 3} (3 x + 4 y)] (4 \hat{i} - 3 \hat{j}) N / C$

The associated magnetic field in Tesla is: [2025]

Q 14 :

A plane electromagnetic wave of frequency 20 MHz travels in free space along the +x direction. At a particular point in space and time, the electric field vector of the wave is $E_{y} = 9.3 {Vm}^{- 1}$ . Then, the magnetic field vector of the wave at the point is [2025]

Q 15 :

The magnetic field of an E.M. wave is given by

$\vec{B} = (\frac{\sqrt{3}}{2} \hat{i} + \frac{1}{2} \hat{j}) 30 \sin [ω (t - \frac{z}{c})]$ (SI Units)

The corresponding electric field in S.I. units is: [2025]

Q 16 :

A plane electromagnetic wave propagates along the +x direction in free space. The components of the electric field, $\vec{E}$ and magnetic field, $\vec{B}$ vectors associated with the wave in Cartesian frame are: [2025]

Q 17 :

If $ε_{0}$ denotes the permittivity of free space and $Φ_{E}$ is the flux of the electric field through the area bounded by the closed surface, then dimension of $(ε_{0} \frac{d ϕ_{E}}{d t})$ are that of: [2025]

Q 21 :

A plane electromagnetic wave of frequency 20 MHz propagates in free space along $x$ -direction. At a particular space and time, $\vec{E} = 6.6 \hat{j} V/m$ . What is $\vec{B}$ at this point? [2023]

Q 22 :

Which of the following Maxwell’s equations is valid for time varying conditions but not valid for static conditions? [2023]

Q 23 :

The source of time varying magnetic field may be [2023]

(A) a permanent magnet
(B) an electric field changing linearly with time
(C) direct current
(D) a decelerating charge particle
(E) an antenna fed with a digital signal

Choose the correct answer from the options given below:

Q 24 :

In an electromagnetic wave, at an instant and at a particular position, the electric field is along the negative $z$ -axis and magnetic field is along the positive $x$ -axis. Then the direction of propagation of electromagnetic wave is [2023]

Q 25 :

To radiate EM signal of wavelength $λ$ with high efficiency, the antennas should have a minimum size equal to [2023]

Q 28 :

The electric field in a plane electromagnetic wave is given by :

$E_{y} = 69 \sin [0.6 \times 10^{3} x - 1.8 \times 10^{11} t] V / m$

The expression for magnetic field associated with this electromagnetic wave is ________ T. [2026]

Q 30 :

A plane electromagnetic wave is moving in free space with velocity $c = 3 \times 10^{8} m/s$ and its electric field is given as $\vec{E} = 54 \sin (k z - ω t) \hat{j} V/m,$ where $\hat{j}$ is the unit vector along y-axis. The magnetic field vector $\vec{B}$ of the wave is: [2026]

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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	$\oint \vec{B} \cdot \vec{d} l = μ_{0} I$

	List I		List II
A.	Gauss’s Law in Electrostatics	I.	$\oint \vec{E} \cdot d \vec{l} = - \frac{d ϕ_{B}}{d t}$
B.	Faraday’s Law	II.	$\oint \vec{B} \cdot d \vec{A} = 0$
C.	Gauss’s Law in Magnetism	III.	$\oint \vec{B} \cdot d \vec{l} = μ_{0} i_{c} + μ_{0} ε_{0} \frac{d ϕ_{E}}{d t}$
D.	Ampere-Maxwell Law	IV.	$\oint \vec{E} \cdot d \vec{S} = \frac{q}{ε_{0}}$

	List – I		List – II
	(Relation)		(Law)
A.	$\oint \vec{E} \cdot d \vec{l} = - \frac{d}{d t} \oint \vec{B} \cdot \vec{d a}$	I.	Ampere’s circuital law
B.	$\oint \vec{B} \cdot \vec{d l} = μ_{0} (I + ε_{0} \frac{d Φ_{E}}{d t})$	II.	Faraday’s laws of electromagnetic induction
C.	$\oint \vec{E} \cdot \vec{d a} = \frac{1}{ε_{0}} \int_{V} ρ d V$	III.	Ampere–Maxwell law
D.	$\oint \vec{B} \cdot \vec{d l} = μ_{0} I$	IV.	Gauss’s law of electrostatics

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]

Q 11 : A parallel plate capacitor has a capacitance C=200 pF. It is connected to 230 V AC supply with an angular frequency 300 rad/s. The RMS value of conduction current in the circuit and displacement current in the capacitor respectively are [2024]

(4)

Q 12 : The electric field in an electromagnetic wave is given by E→=i^ 40cosω(t-zc) NC-1. The magnetic field induction of this wave is (in SI unit): [2024]

Q 13 : The electric field of an electromagnetic wave in free space is E→=57 cos [7.5×106t–5×10–3(3x+4y)](4i^–3j^)N/C The associated magnetic field in Tesla is: [2025]

Q 14 : A plane electromagnetic wave of frequency 20 MHz travels in free space along the +x direction. At a particular point in space and time, the electric field vector of the wave is Ey=9.3 Vm–1. Then, the magnetic field vector of the wave at the point is [2025]

Q 15 : The magnetic field of an E.M. wave is given by B→=(32i^+12j^)30sin[ω(t–zc)] (SI Units) The corresponding electric field in S.I. units is: [2025]

Q 16 : A plane electromagnetic wave propagates along the +x direction in free space. The components of the electric field, E→ and magnetic field, B→ vectors associated with the wave in Cartesian frame are: [2025]

Q 17 : If ε0 denotes the permittivity of free space and ΦE is the flux of the electric field through the area bounded by the closed surface, then dimension of (ε0dϕEdt) are that of: [2025]

Q 21 : A plane electromagnetic wave of frequency 20 MHz propagates in free space along x-direction. At a particular space and time, E→=6.6j^ V/m. What is B→ at this point? [2023]

Q 22 : Which of the following Maxwell’s equations is valid for time varying conditions but not valid for static conditions? [2023]

Q 23 : The source of time varying magnetic field may be [2023] (A) a permanent magnet (B) an electric field changing linearly with time (C) direct current (D) a decelerating charge particle (E) an antenna fed with a digital signal Choose the correct answer from the options given below:

Q 24 : In an electromagnetic wave, at an instant and at a particular position, the electric field is along the negative z-axis and magnetic field is along the positive x-axis. Then the direction of propagation of electromagnetic wave is [2023]

Q 25 : To radiate EM signal of wavelength λ with high efficiency, the antennas should have a minimum size equal to [2023]

Q 26 : In a medium the speed of light wave decreases to 0.2 times to its speed in free space. The ratio of relative permittivity to the refractive index of the medium is x:1. The value of x is _______. (Given speed of light in free space =3×108 ms-1 and for the given medium μr=1) [2023]

Q 28 : The electric field in a plane electromagnetic wave is given by : Ey=69sin [0.6×103x-1.8×1011t]V/m The expression for magnetic field associated with this electromagnetic wave is ________ T. [2026]

Q 29 : The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by Ey=20sin(3×106x-4.5×1014t)V/m, (where x, t and other values have S.I. units). The dielectric constant of the medium is __________. (Speed of light in free space 3×108 m/s) [2026]

Q 30 : A plane electromagnetic wave is moving in free space with velocity c=3×108 m/s and its electric field is given as E→=54sin(kz-ωt)j^ V/m, where j^ is the unit vector along y-axis. The magnetic field vector B→ of the wave is: [2026]

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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]

Q 11 :

A parallel plate capacitor has a capacitance $C = 200$ $p F$ . It is connected to 230 V AC supply with an angular frequency 300 rad/s. The RMS value of conduction current in the circuit and displacement current in the capacitor respectively are [2024]

Q 12 :

The electric field in an electromagnetic wave is given by $\vec{E} = \hat{i} 40 \cos ω (t - \frac{z}{c}) {NC}^{- 1}$ . The magnetic field induction of this wave is (in SI unit): [2024]

Q 13 :

The electric field of an electromagnetic wave in free space is

$\vec{E} = 57 \cos [7.5 \times 10^{6} t - 5 \times 10^{- 3} (3 x + 4 y)] (4 \hat{i} - 3 \hat{j}) N / C$

The associated magnetic field in Tesla is: [2025]

Q 14 :

A plane electromagnetic wave of frequency 20 MHz travels in free space along the +x direction. At a particular point in space and time, the electric field vector of the wave is $E_{y} = 9.3 {Vm}^{- 1}$ . Then, the magnetic field vector of the wave at the point is [2025]

Q 15 :

The magnetic field of an E.M. wave is given by

$\vec{B} = (\frac{\sqrt{3}}{2} \hat{i} + \frac{1}{2} \hat{j}) 30 \sin [ω (t - \frac{z}{c})]$ (SI Units)

The corresponding electric field in S.I. units is: [2025]

Q 16 :

A plane electromagnetic wave propagates along the +x direction in free space. The components of the electric field, $\vec{E}$ and magnetic field, $\vec{B}$ vectors associated with the wave in Cartesian frame are: [2025]

Q 17 :

If $ε_{0}$ denotes the permittivity of free space and $Φ_{E}$ is the flux of the electric field through the area bounded by the closed surface, then dimension of $(ε_{0} \frac{d ϕ_{E}}{d t})$ are that of: [2025]

Q 21 :

A plane electromagnetic wave of frequency 20 MHz propagates in free space along $x$ -direction. At a particular space and time, $\vec{E} = 6.6 \hat{j} V/m$ . What is $\vec{B}$ at this point? [2023]

Q 22 :

Which of the following Maxwell’s equations is valid for time varying conditions but not valid for static conditions? [2023]

Q 23 :

The source of time varying magnetic field may be [2023]

(A) a permanent magnet
(B) an electric field changing linearly with time
(C) direct current
(D) a decelerating charge particle
(E) an antenna fed with a digital signal

Choose the correct answer from the options given below:

Q 24 :

In an electromagnetic wave, at an instant and at a particular position, the electric field is along the negative $z$ -axis and magnetic field is along the positive $x$ -axis. Then the direction of propagation of electromagnetic wave is [2023]

Q 25 :

To radiate EM signal of wavelength $λ$ with high efficiency, the antennas should have a minimum size equal to [2023]

Q 28 :

The electric field in a plane electromagnetic wave is given by :

$E_{y} = 69 \sin [0.6 \times 10^{3} x - 1.8 \times 10^{11} t] V / m$

The expression for magnetic field associated with this electromagnetic wave is ________ T. [2026]

Q 30 :

A plane electromagnetic wave is moving in free space with velocity $c = 3 \times 10^{8} m/s$ and its electric field is given as $\vec{E} = 54 \sin (k z - ω t) \hat{j} V/m,$ where $\hat{j}$ is the unit vector along y-axis. The magnetic field vector $\vec{B}$ of the wave is: [2026]