Electromagnetic Theory MCQs Question and Answer in Engineering Physics

1.
Which one of the following current densities, $$\overrightarrow {\bf{J}} $$ can generate the magnetic vector potential $$\overrightarrow {\bf{A}} = \left( {{y^2}{\bf{\hat i}} + {x^2}{\bf{\hat j}}} \right)?$$

A. $$\frac{2}{{{\mu _0}}}\left( {x{\bf{\hat i}} + y{\bf{\hat j}}} \right)$$

B. $$ - \frac{2}{{{\mu _0}}}\left( {{\bf{\hat i}} + {\bf{\hat J}}} \right)$$

C. $$ - \frac{2}{{{\mu _0}}}\left( {{\bf{\hat i}} - {\bf{\hat j}}} \right)$$

D. $$\frac{2}{{{\mu _0}}}\left( {x{\bf{\hat i}} - y{\bf{\hat j}}} \right)$$

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2.
A metal has free-electron density n = 10²⁹ m^-3. Which of the following wavelengths will excite plasma oscillations?

A. 0.033 μm

B. 0.330 μm

C. 3.300 μm

D. 33.000 μm

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3.
The electric field of a plane electromagnetic wave is $$\overrightarrow {\bf{E}} = \overrightarrow {{{\bf{E}}_0}} \exp \left[ {i\left( {{\bf{\hat x}}k\cos \alpha + {\bf{\hat y}}k\sin \alpha - \omega t} \right)} \right].$$ If $${\bf{\hat x}},\,{\bf{\hat y}}$$ and $${{\bf{\hat z}}}$$ are cartesian unit vectors, the wave vector $$\overrightarrow {\bf{k}} $$ of the electromagnetic wave is

A. $${\bf{\hat z}}k$$

B. $${\bf{\hat x}}k\sin \alpha + {\bf{\hat y}}k\cos \alpha $$

C. $${\bf{\hat x}}k\cos \alpha + {\bf{\hat y}}k\cos \alpha $$

D. $$ - {\bf{\hat z}}k$$

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4.
The dispersion relation for a, low density plasma is ω² = ω₀² + c² k², where ω₀ is the plasma frequency and c is the speed of light in free space. The relationship between the group velocity (v_g) and phase velocity (v_p) is

A. v_p = v_g

B. v_p = $${\text{v}}_{\text{g}}^{\frac{1}{2}}$$

C. v_p v_g = c²

D. v_g = $${\text{v}}_{\text{p}}^{\frac{1}{2}}$$

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5.
Aspherical conductor of radius a is placed in a uniform electric field $$\overrightarrow {\bf{E}} = {E_0}\,{\bf{\hat k}}.$$ The potential at a point P(r, θ) for r > a, is given by $$\phi \left( {r,\,\theta } \right) = {\text{constant}} - {E_0}r\cos \theta + \frac{{{E_0}{a^3}}}{{{r^2}}}\cos \theta $$
where, r is the distance of P from the centre O of the sphere and θ is the angle, OP makes with the Z-axis.

The charge density on the sphere at θ = 30° is

A. $$3\sqrt 3 {\varepsilon _0}\,{E_0}/2$$

B. $$3{\varepsilon _0}\,{E_0}/2$$

C. $$\sqrt 3 {\varepsilon _0}\,{E_0}/2$$

D. $${\varepsilon _0}\,{E_0}/2$$

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6.
A non-relativistic charged particle moves along the positive X-axis with a constant positive acceleration $$a{\bf{\hat x}}.$$ The particle is at the origin at t = 0. Radiation is observed at t = 0 at a distant point (0, d, 0) on the Y-axis. Which one of the following statements is correct?

A. The radiation is unpolarized

B. The radiation is plane polarized with polarization parallel to the X-axis

C. The radiation is plane polarized with polarization parallel to the XY-plane along a line inclined to the X-axis

D. The radiation is elliptically polarized

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7.
In a non-conducting medium characterized by ε = ε₀, μ = μ₀ and conductivity σ = 0, the electric field (in V/m) is given by $$\overrightarrow {\bf{E}} = 20\sin \left[ {{{10}^8}t - kz} \right]{\bf{\hat j}}.$$ The magnetic field $$\overrightarrow {\bf{H}} $$ (in A/m), is given by

A. $$20k\cos \left[ {{{10}^8}t - kz} \right]{\bf{\hat j}}$$

B. $$\frac{{20k}}{{{{10}^8}{\mu _0}}}\sin \left[ {{{10}^8}t - kz} \right]{\bf{\hat j}}$$

C. $$ - \frac{{20k}}{{{{10}^8}{\mu _0}}}\sin \left[ {{{10}^8}t - kz} \right]{\bf{\hat i}}$$

D. $$ - 20k\cos \left[ {{{10}^8}t - kz} \right]{\bf{\hat j}}$$

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8.
An electromagnetic wave with $$\overrightarrow {\bf{E}} \left( {z,\,t} \right) = {E_0}\cos \left( {\omega t - kz} \right){\bf{\hat i}}$$ is travelling in free space and crosses a disc of radius 2 m placed perpendicular to the Z-axis. If E₀ = 60 V/m, the average power in watt, crossing the disc along the Z-direction is

A. 30

B. 60

C. 120

D. 270

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9.
A charged capacitor (C) is connected in series with an inductor (L). When the displacement current reduces to zero, the energy of the LC circuit is

A. stored entirely in its magnetic field

B. stored entirely in its electric field

C. distributed equally among its electric and magnetic fields

D. radiated out of the circuit

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10.
In an electromagnetic field, which one of the following remains invariant under Lorentz transformation?

A. $$\overrightarrow {\bf{E}} \times \overrightarrow {\bf{B}} $$

B. E² - c²B²

C. B²

D. E²

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Electromagnetic Theory MCQs Question and Answer in Engineering Physics

1. Which one of the following current densities, $$\overrightarrow {\bf{J}} $$ can generate the magnetic vector potential $$\overrightarrow {\bf{A}} = \left( {{y^2}{\bf{\hat i}} + {x^2}{\bf{\hat j}}} \right)?$$

Answer & Solution

2. A metal has free-electron density n = 1029 m-3. Which of the following wavelengths will excite plasma oscillations?

Answer & Solution

Answer & Solution

4. The dispersion relation for a, low density plasma is ω2 = ω02 + c2 k2, where ω0 is the plasma frequency and c is the speed of light in free space. The relationship between the group velocity (vg) and phase velocity (vp) is

Answer & Solution

Answer & Solution

6. A non-relativistic charged particle moves along the positive X-axis with a constant positive acceleration $$a{\bf{\hat x}}.$$ The particle is at the origin at t = 0. Radiation is observed at t = 0 at a distant point (0, d, 0) on the Y-axis. Which one of the following statements is correct?

Answer & Solution

7. In a non-conducting medium characterized by ε = ε0, μ = μ0 and conductivity σ = 0, the electric field (in V/m) is given by $$\overrightarrow {\bf{E}} = 20\sin \left[ {{{10}^8}t - kz} \right]{\bf{\hat j}}.$$ The magnetic field $$\overrightarrow {\bf{H}} $$ (in A/m), is given by

Answer & Solution

Answer & Solution

9. A charged capacitor (C) is connected in series with an inductor (L). When the displacement current reduces to zero, the energy of the LC circuit is

Answer & Solution

10. In an electromagnetic field, which one of the following remains invariant under Lorentz transformation?

Answer & Solution

1.
Which one of the following current densities, $$\overrightarrow {\bf{J}} $$ can generate the magnetic vector potential $$\overrightarrow {\bf{A}} = \left( {{y^2}{\bf{\hat i}} + {x^2}{\bf{\hat j}}} \right)?$$

2.
A metal has free-electron density n = 10²⁹ m^-3. Which of the following wavelengths will excite plasma oscillations?

4.
The dispersion relation for a, low density plasma is ω² = ω₀² + c² k², where ω₀ is the plasma frequency and c is the speed of light in free space. The relationship between the group velocity (v_g) and phase velocity (v_p) is

6.
A non-relativistic charged particle moves along the positive X-axis with a constant positive acceleration $$a{\bf{\hat x}}.$$ The particle is at the origin at t = 0. Radiation is observed at t = 0 at a distant point (0, d, 0) on the Y-axis. Which one of the following statements is correct?

7.
In a non-conducting medium characterized by ε = ε₀, μ = μ₀ and conductivity σ = 0, the electric field (in V/m) is given by $$\overrightarrow {\bf{E}} = 20\sin \left[ {{{10}^8}t - kz} \right]{\bf{\hat j}}.$$ The magnetic field $$\overrightarrow {\bf{H}} $$ (in A/m), is given by

9.
A charged capacitor (C) is connected in series with an inductor (L). When the displacement current reduces to zero, the energy of the LC circuit is

10.
In an electromagnetic field, which one of the following remains invariant under Lorentz transformation?