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)

$E = E_{0} \sin (ω t - k x)$

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

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

Q 11 :

The electric field in an electromagnetic wave is given as $\vec{E} = 20 \sin ω (t - \frac{x}{c}) \hat{j} {NC}^{- 1}$

Where $ω$ and $c$ are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of $5 \times 10^{- 4} m^{3}$ will be

(Given $ε_{0} = 8.85 \times 10^{- 12} C^{2} / {Nm}^{2}$ ) [2023]

$28.5 \times 10^{- 13} J$
$17.7 \times 10^{- 13} J$
$8.85 \times 10^{- 13} J$
$88.5 \times 10^{- 13} J$

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(3)

$\vec{E} = 20 \sin ω (t - \frac{x}{c}) \hat{j} {NC}^{- 1}$

$Average energy density of an EM wave = \frac{1}{2} ε_{0} E_{0}^{2}$

$Energy stored = (\frac{1}{2} ε_{0} E_{0}^{2}) (Volume)$

$= \frac{1}{2} \times 8.85 \times 10^{- 12} \times {(20)}^{2} \times (5 \times 10^{- 4}) J$

$= 8.85 \times 10^{- 13} J$

Q 12 :

The equation of the electric field of an electromagnetic wave propagating through free space is given by:

$E = \sqrt{377} \sin (6.27 \times 10^{3} t - 2.09 \times 10^{- 5} x) N/C$

The average power of the electromagnetic wave is $(\frac{1}{α}) {W/m}^{2} .$ The value of $α$ is _________.

$(Take \sqrt{\frac{μ_{0}}{ε_{0}}} = 377 in SI units)$ [2026]

(2)

Here, $v = \frac{ω}{K} = \frac{6.27 \times 10^{3}}{2.09 \times 10^{- 5}} = 3 \times 10^{8}$

So, wave moving in vacuum.

Now, $I = (\frac{1}{2} ε_{0} E_{0}^{2}) c = \frac{1}{2} ε_{0} E_{0}^{2} \frac{1}{\sqrt{μ_{0} ε_{0}}}$

$= \frac{1}{2} \sqrt{\frac{ε_{0}}{μ_{0}}} E_{0}^{2} = \frac{1}{2} \times \frac{1}{377} \times 377$

$\frac{1}{d} = \frac{1}{2}$

$d = 2$

Q 13 :

A laser beam has intensity of $4.0 \times 10^{14} {W/m}^{2}$ . The amplitude of magnetic field associated with beam is ______ T.
$(Take ε_{0} = 8.85 \times 10^{- 12}, C^{2} / N m^{2}$ and $c = 3 \times 10^{8} m/s)$ [2026]

2.0
18.3
5.5
1.83

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(4)

$I = \frac{1}{2} ε_{0} E_{0}^{2} \cdot C$

$∴$ $E_{0} = \sqrt{\frac{2 I}{ε_{0} C}}$

$& \frac{E_{0}}{B_{0}} = C$

$∴$ $B_{0} = \frac{E_{0}}{C} = \frac{1}{C} \sqrt{\frac{2 I}{ε_{0} C}}$

$∴$ $B_{0} = \frac{1}{3 \times 10^{8}} \sqrt{\frac{2 \times 4 \times 10^{14}}{8.85 \times 10^{- 12} \times 3 \times 10^{8}}}$

$B_{0} = \frac{10}{3} \sqrt{\frac{8}{8.85 \times 3}}$

$B_{0} = 1.83 T$

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]

Q 13 :

A laser beam has intensity of $4.0 \times 10^{14} {W/m}^{2}$ . The amplitude of magnetic field associated with beam is ______ T.
$(Take ε_{0} = 8.85 \times 10^{- 12}, C^{2} / N m^{2}$ and $c = 3 \times 10^{8} m/s)$ [2026]

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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]

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=E0sin(ωt-kx) and B=B0sin(ωt-kx), the ratio of average electric energy density to average magnetic energy density is [2023]

Q 9 : The energy density associated with electric field E→ and magnetic field B→ of an electromagnetic wave in free-space is given by (ε0-permittivity of free space, μ0-permeability of free space) [2023]

Q 10 : The energy of an electromagnetic wave contained in a small volume oscillates with [2023]

Q 11 : The electric field in an electromagnetic wave is given as E→=20sinω(t-xc)j^ NC-1 Where ω and c are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of 5×10-4 m3 will be (Given ε0=8.85×10-12 C2/Nm2) [2023]

Q 12 : The equation of the electric field of an electromagnetic wave propagating through free space is given by: E=377 sin(6.27×103 t-2.09×10-5 x) N/C The average power of the electromagnetic wave is (1α) W/m2. The value of α is _________. (Take μ0ε0=377 in SI units) [2026]

Q 13 : A laser beam has intensity of 4.0×1014 W/m2. The amplitude of magnetic field associated with beam is ______ T. (Take ε0=8.85×10-12, C2/Nm2 and c=3×108 m/s) [2026]

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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]

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]

Q 13 :

A laser beam has intensity of $4.0 \times 10^{14} {W/m}^{2}$ . The amplitude of magnetic field associated with beam is ______ T.
$(Take ε_{0} = 8.85 \times 10^{- 12}, C^{2} / N m^{2}$ and $c = 3 \times 10^{8} m/s)$ [2026]