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

(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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3

4

(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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4

(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)

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

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

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]

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Topic Question Set

Q 1 : In the given electromagnetic wave Ey=600sin(ωt-kx)Vm-1, intensity of the associated light beam is (in W/m2) (Given ε0=9×10-12C2N-1m-2) [2024]

Q 2 : A plane electromagnetic wave propagating in x-direction is described by Ey=(200 Vm-1)sin[1.5×107t-0.05x]; The intensity of the wave is (Use ε0=8.85×10-12C2N-1m-2) [2024]

Q 3 : In a plane EM wave, the electric field oscillates sinusoidally at a frequency of 5×1010Hz and an amplitude of 50Vm-1. The total average energy density of the electromagnetic field of the wave is [Use ε0=8.85×10-12C2/Nm2] [2024]

Q 5 : The unit of 2Iε0c is: (I = intensity of an electromagnetic wave, c : speed of light) [2025]

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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]