Electromagnetic Waves | Physics JEE Main questions with Solutions

Q 1 :

In the given electromagnetic wave $E_{y} = 600 \sin (ω t - k x) V m^{- 1}$ , intensity of the associated light beam is (in $W / m^{2}$ )

(Given $ε_{0} = 9 \times 10^{- 12} C^{2} N^{- 1} m^{- 2}$ ) [2024]

729
243
972
486

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(4)

Intensity, $I = \frac{1}{2} ϵ_{0} E_{0}^{2} c \Rightarrow I = \frac{9}{2} \times 36 \times 3 = 486 W / m^{2}$

Q 2 :

A plane electromagnetic wave propagating in x-direction is described by

$E_{y} = (200 V m^{- 1}) \sin [1.5 \times 10^{7} t - 0.05 x];$

The intensity of the wave is

(Use $ε_{0} = 8.85 \times 10^{- 12} C^{2} N^{- 1} m^{- 2}$ ) [2024]

$35.4$ $W m^{- 2}$
$53.1$ $W m^{- 2}$
$26.2$ $W m^{- 2}$
$106.2$ $W m^{- 2}$

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(2)

$I = \frac{1}{2} ε_{0} E_{0}^{2} \times c$

$I = 53.1$ $W / m^{2}$

Q 3 :

In a plane EM wave, the electric field oscillates sinusoidally at a frequency of $5 \times 10^{10} H z$ and an amplitude of $50 V m^{- 1}$ . The total average energy density of the electromagnetic field of the wave is [Use $ε_{0} = 8.85 \times 10^{- 12} C^{2} / N m^{2}$ ] [2024]

$1.106 \times 10^{- 8} J m^{- 3}$
$2.212 \times 10^{- 10} J m^{- 3}$
$4.425 \times 10^{- 8} J m^{- 3}$
$2.212 \times 10^{- 8} J m^{- 3}$

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(1)

$U_{E} = \frac{1}{2} ϵ_{0} E^{2}$

$U_{E} = \frac{1}{2} \times 8.85 \times 10^{- 12} \times {(50)}^{2} = 1.106 \times 10^{- 8} J / m^{3}$

Q 4 :

Due to presence of an em-wave whose electric component is given by E = 100 sin ( $ω$ t – kx) ${NC}^{- 1}$ , a cylinder of length 200 cm holds certain amount of em-energy inside it. If another cylinder of same length but half diameter than previous one holds same amount of em-energy, the magnitude of the electric field of the corresponding em-wave should be modified as [2025]

25 sin ( $ω$ t – kx) ${NC}^{- 1}$
200 sin ( $ω$ t – kx) ${NC}^{- 1}$
400 sin ( $ω$ t – kx) ${NC}^{- 1}$
50 sin ( $ω$ t – kx) ${NC}^{- 1}$

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(2)

Energy density of an ${EM}_{wave}$ $= \frac{1}{2} ε_{0} E_{0}^{2},$ where $E_{0}$ is the amplitude of the wave.

Since total energy is the same for both cylinders

$(\frac{1}{2} ε_{0} E_{1}^{2}) π R_{1}^{2} L_{1} = (\frac{1}{2} ε_{0} E_{2}^{2}) π R_{2}^{2} L_{2}$

$\Rightarrow E_{1}^{2} R_{1}^{2} L_{1} = E_{2}^{2} R_{2}^{2} L_{2}$

or $E_{2} = \frac{E_{1} R_{1}}{R_{2}} \sqrt{\frac{L_{1}}{L_{2}}} = \frac{100 d}{(d / 2)} \sqrt{\frac{L_{1}}{L_{1}}} = 200 N/C [∵ L_{1} = L_{2} = 200 cm]$

$\Rightarrow The amplitude of corresponding electromagnetic wave is 200 N/C.$

Hence the wave is, $E = 200 \sin (ω t - k x) {NC}^{- 1} .$

Q 5 :

The unit of $\sqrt{\frac{2 I}{ε_{0} c}}$ is:

( $I$ = intensity of an electromagnetic wave, c : speed of light) [2025]

Vm
NC
Nm
${NC}^{- 1}$

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(4)

$I = \frac{1}{2} ε_{0} E_{0}^{2} \times c \Rightarrow E_{0} = \sqrt{\frac{2 I}{ε_{0} c}}$

$E_{0} : electric field (N/C)$

Q 6 :

An electromagnetic wave is transporting energy in the negative ‘z’ direction. At a certain point and certain time the direction of electric field of the wave is along positive ‘y’ direction. What will be direction of the magnetic field of the wave at that point and instant? [2023]

Positive direction of ‘z’
Negative direction of ‘y’
Positive direction of ‘x’
Negative direction of ‘x’

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(3)

$\bar{S} = - \hat{k}, \bar{E} = \hat{j}, \bar{B} = ?$

$\bar{S} = \bar{E} \times \bar{B}$

Here $\bar{B}$ should be along positive $x$ -direction.

Q 7 :

The ratio of average electric energy density and total average energy density of electromagnetic wave is [2023]

$2$
$1$
$3$
$\frac{1}{2}$

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(4)

$⟨ u_{E} ⟩ = ⟨ u_{B} ⟩ = \frac{1}{2} ⟨ u_{total} ⟩$

$So \frac{⟨ u_{E} ⟩}{⟨ u_{total} ⟩} = \frac{1}{2}$

Q 8 :

For the plane electromagnetic wave given by $E = E_{0} \sin (ω t - k x) and B = B_{0} \sin (ω t - k x),$ the ratio of average electric energy density to average magnetic energy density is [2023]

1
2
4
1/2

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(1)

$\frac{Electric energy density}{Magnetic energy density} = \frac{\frac{1}{2} ε_{0} E_{rms}^{2}}{(\frac{B_{rms}^{2}}{2 μ_{0}})}$
$= {(\frac{E_{rms}}{B_{rms}})}^{2} \cdot μ_{0} ε_{0} [c = \frac{1}{μ_{0} ε_{0}}]$

$= \frac{c^{2}}{c^{2}} = 1$

Q 9 :

The energy density associated with electric field $\vec{E}$ and magnetic field $\vec{B}$ of an electromagnetic wave in free-space is given by ( $ε_{0}$ -permittivity of free space, $μ_{0}$ -permeability of free space) [2023]

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

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(4)

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

Q 10 :

The energy of an electromagnetic wave contained in a small volume oscillates with [2023]

zero frequency
half the frequency of the wave
double the frequency of the wave
the frequency of the wave

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(3)

$E = E_{0} \sin (ω t - k x)$

$Energy density (\frac{d u}{d v}) = ε_{0} E_{0}^{2} \sin^{2} (ω t - k x)$

$= \frac{ε_{0} E_{0}^{2}}{2} [1 - \cos (2 ω t - 2 k x)]$

Topic Question Set

Q 1 :

In the given electromagnetic wave $E_{y} = 600 \sin (ω t - k x) V m^{- 1}$ , intensity of the associated light beam is (in $W / m^{2}$ )

(Given $ε_{0} = 9 \times 10^{- 12} C^{2} N^{- 1} m^{- 2}$ ) [2024]

Q 2 :

A plane electromagnetic wave propagating in x-direction is described by

$E_{y} = (200 V m^{- 1}) \sin [1.5 \times 10^{7} t - 0.05 x];$

The intensity of the wave is

(Use $ε_{0} = 8.85 \times 10^{- 12} C^{2} N^{- 1} m^{- 2}$ ) [2024]

Q 3 :

In a plane EM wave, the electric field oscillates sinusoidally at a frequency of $5 \times 10^{10} H z$ and an amplitude of $50 V m^{- 1}$ . The total average energy density of the electromagnetic field of the wave is [Use $ε_{0} = 8.85 \times 10^{- 12} C^{2} / N m^{2}$ ] [2024]

Q 5 :

The unit of $\sqrt{\frac{2 I}{ε_{0} c}}$ is:

( $I$ = intensity of an electromagnetic wave, c : speed of light) [2025]

Q 6 :

An electromagnetic wave is transporting energy in the negative ‘z’ direction. At a certain point and certain time the direction of electric field of the wave is along positive ‘y’ direction. What will be direction of the magnetic field of the wave at that point and instant? [2023]

Q 7 :

The ratio of average electric energy density and total average energy density of electromagnetic wave is [2023]

Q 8 :

For the plane electromagnetic wave given by $E = E_{0} \sin (ω t - k x) and B = B_{0} \sin (ω t - k x),$ the ratio of average electric energy density to average magnetic energy density is [2023]

Q 9 :

The energy density associated with electric field $\vec{E}$ and magnetic field $\vec{B}$ of an electromagnetic wave in free-space is given by ( $ε_{0}$ -permittivity of free space, $μ_{0}$ -permeability of free space) [2023]

Q 10 :

The energy of an electromagnetic wave contained in a small volume oscillates with [2023]

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