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Electromagnetic Waves Set-2 MCQ Online Practice Test | Class 12 | Quiz Tweek

Electromagnetic Waves Set-2

Practice Important MCQs for Electromagnetic Waves — Physics, Class 12.

Electromagnetic waves form a bridge between Maxwell's equations and real-world phenomena such as radiation, optics, and signal transmission; questions on energy flow (Poynting vector), dispersion, boundary conditions, and wave propagation in media are frequently tested in CBSE board papers and form a staple of JEE/NEET problem-solving. Building a strong conceptual and problem-solving grasp of this chapter improves ability to handle multi-step numerical problems, graph interpretation and assertion–reason type reasoning that competitive exams emphasize.

This set focuses on reasoning-intensive problems — combining algebraic manipulations, physical interpretation, and data/graph analysis — so students practice translating Maxwellian concepts into calculable results and spotting common misconceptions (evanescent behaviour, phase vs. group velocity, skin depth, standing-wave nodes) that appear in higher-difficulty questions.

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Q1. A plane electromagnetic wave in vacuum has electric field amplitude $E_0=300\ \mathrm{V\,m^{-1}}$ . Calculate the time-averaged Poynting flux (intensity) $\langle S\rangle$ carried by this wave. Use $\mu_0=4\pi\times10^{-7}\ \mathrm{H\,m^{-1}}$ and $c=3.0\times10^8\ \mathrm{m\,s^{-1}}$ .

(A)

$2.39\times10^{1}\ \mathrm{W\,m^{-2}}$

(B)

$1.19\times10^{2}\ \mathrm{W\,m^{-2}}$

(C)

$3.00\times10^{3}\ \mathrm{W\,m^{-2}}$

(D)

$2.39\times10^{2}\ \mathrm{W\,m^{-2}}$

Q2. Assertion (A): In a good conductor the amplitude of an electromagnetic wave decays exponentially with a penetration depth (skin depth) that is independent of frequency. Reason (R): The skin depth in a conductor is given by $\delta=\sqrt{\dfrac{2}{\omega\mu\sigma}}$ , so it depends on angular frequency $\omega$ .

(A)

Both A and R are true and R is the correct explanation of A.

(B)

Both A and R are true but R is not the correct explanation of A.

(C)

A is true but R is false.

(D)

A is false but R is true.

Q3. A plane electromagnetic wave in vacuum has magnetic field amplitude $B_0=2.0\times10^{-6}\ \mathrm{T}$ . What is the time-averaged total energy density $\langle u\rangle$ (electric + magnetic) in the wave? Use $\mu_0=4\pi\times10^{-7}\ \mathrm{H\,m^{-1}}$ .

(A)

$6.37\times10^{-6}\ \mathrm{J\,m^{-3}}$

(B)

$1.59\times10^{-6}\ \mathrm{J\,m^{-3}}$

(C)

$3.18\times10^{-6}\ \mathrm{J\,m^{-3}}$

(D)

$7.96\times10^{-7}\ \mathrm{J\,m^{-3}}$

Q4. Inside a conductor the intensity of an electromagnetic wave decays as $I(x)=I_0\exp(-2x/\delta)$ , where $\delta$ is the skin depth. A graph of $\ln(I/I_0)$ vs.\ $x$ (in metres) is a straight line with slope $-200\ \mathrm{m^{-1}}$ . From this graph determine the skin depth $\delta$ .

(A)

$1.0\times10^{-2}\ \mathrm{m}$

(B)

$5.0\times10^{-3}\ \mathrm{m}$

(C)

$1.0\times10^{-1}\ \mathrm{m}$

(D)

$2.0\times10^{-2}\ \mathrm{m}$

Q5. Monochromatic light has wavelength $600\ \mathrm{nm}$ in vacuum. It enters a glass slab with refractive index $n=1.50$ . What is its wavelength inside the glass? (Assume the medium is non-dispersive at this frequency.)

(A)

$900\ \mathrm{nm}$

(B)

$600\ \mathrm{nm}$

(C)

$400\ \mathrm{nm}$

(D)

$150\ \mathrm{nm}$

Q6. A linearly polarized plane wave $\mathbf{E}=E_0\hat{x}\cos(kz-\omega t)$ propagates in $+z$ and is normally incident on an ideal conductor occupying the plane $z=0$ . The incident and reflected waves form a standing wave for $z>0$ . Which statement correctly describes the fields at the conductor surface $z=0$ ?

(A)

Both electric and magnetic fields have nodes at $z=0$ .

(B)

Electric field has a node and magnetic field has an antinode at $z=0$ .

(C)

Electric field has an antinode and magnetic field has a node at $z=0$ .

(D)

Both electric and magnetic fields have antinodes at $z=0$ .

Q7. In a cold electron plasma the dispersion relation is $\omega^2=\omega_p^2+c^2k^2$ . For $\omega=2.0\times10^{11}\ \mathrm{rad\,s^{-1}}$ and $\omega_p=1.0\times10^{11}\ \mathrm{rad\,s^{-1}}$ , calculate the group velocity $v_g=d\omega/dk$ of the wave. Take $c=3.0\times10^8\ \mathrm{m\,s^{-1}}$ .

(A)

$1.50\times10^{8}\ \mathrm{m\,s^{-1}}$

(B)

$2.00\times10^{8}\ \mathrm{m\,s^{-1}}$

(C)

$2.83\times10^{8}\ \mathrm{m\,s^{-1}}$

(D)

$2.60\times10^{8}\ \mathrm{m\,s^{-1}}$

Q8. A medium shows these local behaviours of refractive index $n(\omega)$ around a frequency $\omega_0$ :

Region I: $n$ increases linearly from $1.40$ at $\omega_0-\Delta\omega$ to $1.60$ at $\omega_0+\Delta\omega$ .
Region II: $n$ decreases linearly from $1.60$ at $\omega_0-\Delta\omega$ to $1.50$ at $\omega_0+\Delta\omega$ .
Assuming $\Delta\omega$ and $\omega_0$ are the same in both cases, at which region will the group velocity $v_g=\dfrac{c}{\,n+\omega\,dn/d\omega\,}$ at $\omega_0$ be larger?

(A)

Region I only

(B)

Both regions give the same $v_g$

(C)

Region II only

(D)

Cannot determine without numerical values of $\omega_0$ and $\Delta\omega$

Q9. Assertion (A): In certain frequency ranges of a dispersive medium the phase velocity of electromagnetic waves can exceed the speed of light in vacuum $c$ . Reason (R): Phase velocity exceeding $c$ does not violate special relativity because phase velocity does not represent the velocity of information or energy transfer; the signal or front velocity remains $\le c$ .

(A)

Both A and R are true and R is the correct explanation of A.

(B)

Both A and R are true but R is not the correct explanation of A.

(C)

A is true but R is false.

(D)

A is false but R is true.

Q10. An electromagnetic plane wave with frequency $\omega<\omega_p$ (below the plasma frequency) produces evanescent fields inside a plasma and decays exponentially with depth. Which statement about the time-averaged Poynting vector $\langle\mathbf{S}\rangle$ inside the plasma is correct?

(A)

Its magnitude decreases exponentially with depth, but it remains strictly positive in the propagation direction.

(B)

The time-averaged Poynting vector in the direction of propagation is zero (no net energy transport into the plasma).

(C)

It is negative, indicating net energy flow back toward the source.

(D)

It oscillates in time with zero mean but instantaneous non-zero flux that carries net energy inward.

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