Electromagnetic Waves | Physics JEE Main questions with Solutions

Q 11 :

The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant $k$ = 3 and permeability $μ = 2 μ_{0},$ is

$(μ_{0} =permeability of vacuum)$ [2026]

$\sqrt{6} : 1$
3 : 2
36 : 1
6 : 1

1

2

3

4

(1)

$\frac{C}{V} = μ = \sqrt{ε_{r} μ_{r}}$

$\frac{C}{V} = \sqrt{\frac{3 \times 2}{1}} = \frac{\sqrt{6}}{1}$

Q 12 :

An electromagnetic wave of frequency 100 MHz propagates through a medium of conductivity, $σ = 10 m h o / m$ . The ratio of maximum conduction current density to maximum displacement current density is ______.

$[Take \frac{1}{4 π ε_{0}} = 9 \times 10^{9} {N m}^{2} / C^{2}]$ [2026]

(1800)

$A$

$j_{c} = σ E$

$E \Rightarrow E_{0} \sin (ω t - k x)$

$j_{c} = σ E_{0} \sin (ω t - k x)$

$\Rightarrow {(j_{c})}_{\max} = σ E_{0} . . . (i)$

$J_{d} = \frac{i_{d}}{A} = \frac{1}{A} \times ε_{0} \frac{A d E}{d t}$

$= ε_{0} \times E_{0} ω \cos (ω t - k x)$

${(j_{d})}_{\max} = ε_{0} E_{0} ω . . . (ii)$

(i)/(ii)

$\frac{{(j_{c})}_{\max}}{{(j_{d})}_{\max}} = \frac{σ E_{0}}{ε_{0} ω E_{0}} \Rightarrow \frac{σ}{ε_{0} ω}$

$\Rightarrow \frac{10 \times 4 π \times 9 \times 10^{9}}{2 π \times 100 \times 10^{6}}$

$\Rightarrow 1800$

Q 13 :

The electric field of an electromagnetic wave travelling through a medium is given by $\vec{E} (x, t) = 25 \sin (2.0 \times 10^{15} t - 10^{7} x) \hat{n} .$ Then the refractive index of the medium is _____

(All given measurement are in SI units.) [2026]

1.5
1.7
2
1.2

1

2

3

4

(1)

$ω = 2 \times 10^{15} rad/s$

$k = 10^{7} m^{- 1}$

$v = \frac{2 π}{k} \cdot \frac{ω}{2 π} = \frac{ω}{k} = \frac{2 \times 10^{15}}{10^{7}} = 2 \times 10^{8} = \frac{c}{1.5}$

$\Rightarrow μ = 1.5$

Q 14 :

Match List I With List II

List I List II

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

B) $\oint \vec{E} \cdot d \vec{l} = - \frac{d ϕ_{B}}{d t}$ II. Gauss’ law for magnetism

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

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

Choose the correct answer from the options given below:

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

1

2

3

4

(3)

$Ampere-Maxwell law \to \oint \vec{B} \cdot d \vec{l} = μ_{0} i_{c} + μ_{0} ε_{0} \frac{d ϕ_{E}}{d t}$

$Faraday law \to \oint \vec{E} \cdot d \vec{l} = - \frac{d ϕ_{B}}{d t}$

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

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

Q 15 :

A plane electromagnetic wave travelling in non-magnetic medium is given by

$E = (9 \times 10^{8} N C^{- 1}) \sin [(9 \times 10^{8} r a d s^{- 1}) t - (6 m^{- 1}) x]$

where $x$ is in metre and $t$ is in seconds. The dielectric constant of the medium is ________

(4)

$V = \frac{ω}{k} = \frac{9 \times 10^{8}}{6} = 1.5 \times 10^{8} m / s,$

$Refractive index μ = \frac{C}{V} \Rightarrow \sqrt{K} = \frac{3 \times 10^{8}}{1.5 \times 10^{8}}$

$∴$ $K = 4$

Q 16 :

The electric field of an electromagnetic wave in free space is represented by $\vec{E} = E_{0} \cos (ω t - k z) \hat{i}$ . The corresponding magnetic induction vector will be

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

1

2

3

4

(2)

$\vec{E} \times \vec{B} gives direction of \vec{V}$

Q 17 :

A plane electromagnetic wave of frequency 35 MHz travels in free space along positive 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:

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

1

2

3

4

(1)

$\frac{E}{B} = C$

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

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

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

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

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

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

Topic Question Set

Q 11 :

The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant $k$ = 3 and permeability $μ = 2 μ_{0},$ is

$(μ_{0} =permeability of vacuum)$ [2026]

Q 12 :

An electromagnetic wave of frequency 100 MHz propagates through a medium of conductivity, $σ = 10 m h o / m$ . The ratio of maximum conduction current density to maximum displacement current density is ______.

$[Take \frac{1}{4 π ε_{0}} = 9 \times 10^{9} {N m}^{2} / C^{2}]$ [2026]

Q 13 :

The electric field of an electromagnetic wave travelling through a medium is given by $\vec{E} (x, t) = 25 \sin (2.0 \times 10^{15} t - 10^{7} x) \hat{n} .$ Then the refractive index of the medium is _____

(All given measurement are in SI units.) [2026]

Q 15 :

A plane electromagnetic wave travelling in non-magnetic medium is given by

$E = (9 \times 10^{8} N C^{- 1}) \sin [(9 \times 10^{8} r a d s^{- 1}) t - (6 m^{- 1}) x]$

where $x$ is in metre and $t$ is in seconds. The dielectric constant of the medium is ________

Q 16 :

The electric field of an electromagnetic wave in free space is represented by $\vec{E} = E_{0} \cos (ω t - k z) \hat{i}$ . The corresponding magnetic induction vector will be

Q 17 :

A plane electromagnetic wave of frequency 35 MHz travels in free space along positive 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:

Want Us to Email you About Special Offers & Updates?

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

Topic Question Set

Q 11 : The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant k = 3 and permeability μ=2μ0, is (μ0=permeability of vacuum) [2026]

Q 12 : An electromagnetic wave of frequency 100 MHz propagates through a medium of conductivity,σ=10 mho/m. The ratio of maximum conduction current density to maximum displacement current density is ______. [Take 14πε0=9×109 N m2/C2] [2026]

Q 13 : The electric field of an electromagnetic wave travelling through a medium is given by E→(x,t)=25sin(2.0×1015t-107x)n^. Then the refractive index of the medium is _____ (All given measurement are in SI units.) [2026]

Q 15 : A plane electromagnetic wave travelling in non-magnetic medium is given by E=(9×108 NC-1)sin[(9×108 rad s-1)t-(6 m-1)x] where x is in metre and t is in seconds. The dielectric constant of the medium is ________

Q 16 : The electric field of an electromagnetic wave in free space is represented by E→=E0cos(ωt-kz)i^. The corresponding magnetic induction vector will be

Q 17 : A plane electromagnetic wave of frequency 35 MHz travels in free space along positive X-direction. At a particular point (in space and time) E→=9.6 j^ V/m. The value of magnetic field at this point is:

Want Us to Email you About Special Offers & Updates?

Q 11 :

The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant $k$ = 3 and permeability $μ = 2 μ_{0},$ is

$(μ_{0} =permeability of vacuum)$ [2026]

Q 12 :

An electromagnetic wave of frequency 100 MHz propagates through a medium of conductivity, $σ = 10 m h o / m$ . The ratio of maximum conduction current density to maximum displacement current density is ______.

$[Take \frac{1}{4 π ε_{0}} = 9 \times 10^{9} {N m}^{2} / C^{2}]$ [2026]

Q 13 :

The electric field of an electromagnetic wave travelling through a medium is given by $\vec{E} (x, t) = 25 \sin (2.0 \times 10^{15} t - 10^{7} x) \hat{n} .$ Then the refractive index of the medium is _____

(All given measurement are in SI units.) [2026]

Q 15 :

A plane electromagnetic wave travelling in non-magnetic medium is given by

$E = (9 \times 10^{8} N C^{- 1}) \sin [(9 \times 10^{8} r a d s^{- 1}) t - (6 m^{- 1}) x]$

where $x$ is in metre and $t$ is in seconds. The dielectric constant of the medium is ________

Q 16 :

The electric field of an electromagnetic wave in free space is represented by $\vec{E} = E_{0} \cos (ω t - k z) \hat{i}$ . The corresponding magnetic induction vector will be

Q 17 :

A plane electromagnetic wave of frequency 35 MHz travels in free space along positive 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: