Electromagnetic Theory — Part 1 MCQs with Explanations

$$ - \frac{2}{{{\mu _0}}}\left( {{\bf{\hat i}} + {\bf{\hat J}}} \right)$$ is the correct answer to “Which one of the following current densities, $$\overrightarrow {\bf{J}} $$ can generate the magnetic vector potential $$\overrightarrow {\bf{A}} = \left( {{y^2}{\bf{\hat i}} + {x^2}{\bf{\hat j}}} \right)?$$”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

0.033 μm is the correct answer to “A metal has free-electron density n = 10 29 m -3 . Which of the following wavelengths will excite plasma oscillations”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$${\bf{\hat x}}k\cos \alpha + {\bf{\hat y}}k\cos \alpha $$ is the correct answer to “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”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

vp vg = c2 is the correct answer to “The dispersion relation for a, low density plasma is ω 2 = ω 0 2 + c 2 k 2 , where ω 0 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”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$3\sqrt 3 {\varepsilon _0}\,{E_0}/2$$ is the correct answer to “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”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

The radiation is plane polarized with polarization parallel to the X-axis is the correct answer to “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”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$ - \frac{{20k}}{{{{10}^8}{\mu _0}}}\sin \left[ {{{10}^8}t - kz} \right]{\bf{\hat i}}$$ is the correct answer to “In a non-conducting medium characterized by ε = ε 0 , μ = μ 0 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”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

60 is the correct answer to “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 E 0 = 60 V/m, the average power in watt, crossing the disc along the Z-direction is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

stored entirely in its magnetic field is the correct answer to “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”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

E2 - c2B2 is the correct answer to “In an electromagnetic field, which one of the following remains invariant under Lorentz transformation”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

the electrostatic potential has the same value for r < a is the correct answer to “An electric charge +Q is placed on the surface of a solid conduction sphere of radius a. The distance measured from the centre of the sphere is denoted as r. Then,”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$${\phi _0}$$ is the correct answer to “Consider a conducting loop of radius a and total loop resistance R placed in a region with a magnetic field B thereby enclosing a flux $${\phi _0}$$ . The loop is connected to an electronic circuit as shown, the capacitor being initially uncharged. If the loop is pulled out of the region of the magnetic field at a constant speed u, the final output voltage V out is independent of”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

3ε0 E0 cos θ is the correct answer to “A conducting sphere of radius R is placed in uniform electric field $${\overrightarrow {\bf{E}} _0}$$ directed along +Z-axis. The electric potential for outside points is given as $${V_{{\text{out}}}} = - {E_0}\left( {1 - \frac{{{R^3}}}{{{r^3}}}} \right)r\cos \theta ,$$ where r is the distance from the centre and θ is the polar angle. The charge density on the surface of the sphere is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

0.3 μm is the correct answer to “A laser beam of wavelength 600 nm with a circular cross-section having a radius of 10 mm fails normally on a lens of radius 20 mm and focal length 10 cm. The radius of the focussed spot is approximately”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$\frac{{2\sqrt 2 \,{\mu _0}\,l}}{{\pi a}}{{\hat e}_z}$$ is the correct answer to “A current $$l$$ flows in the anticlockwise direction through a square loop of side a lying in the XOY plane with its centre at the origin. The magnetic induction at the centre of the square loop is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$E \propto \frac{1}{{{r^2}}},\,B \propto \frac{1}{{{r^2}}}$$ is the correct answer to “The electric (E) and magnetic (B) field amplitudes associated with an electromagnetic radiation from a point source behave at a distance r from the source as”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

2000 is the correct answer to “An electron is accelerated from rest by 10.2 millionvolt. The percent increase in its mass is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$\frac{{{\mu _r}{\mu _0}Nl}}{{2\pi r}}$$ is the correct answer to “A toroidal coil has N closely-wound turns. Assume the current through the coil to be $$l$$ and the toroid is filled with a magnetic material of relative permittivity $${\mu _r}.$$ The magnitude of magnetic induction $$\overrightarrow {\bf{B}} $$ inside the toroid, at a radial distance r from the axis, is given by”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$\frac{1}{{2m}}{\left( {\overrightarrow {\bf{p}} - \frac{q}{c}\overrightarrow {\bf{A}} } \right)^2} + q\phi $$ is the correct answer to “A particle of charge q, mass m and linear momentum $$\overrightarrow {\bf{p}} $$ enters an electromagnetic field of vector potential $$\overrightarrow {\bf{A}} $$ and scalar potential $$\phi .$$ The Hamiltonian of the particle is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$ - \frac{{3{\mu _0}}}{{8\pi }} \cdot \frac{{{m^2}}}{{{d^3}}}$$ is the correct answer to “Two magnetic dipoles of magnitude m each are placed in a plane as shown below. The energy of interaction is given by”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$ - 6\,{\phi _0}{\varepsilon _0}$$ is the correct answer to “If the electrostatic potential were Igiven by $$\phi = {\phi _0}$$ (x 2 + y 2 + z 2 ), where $${\phi _0}$$ is constant, then the charge density giving rise to the above potential would be”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$\overrightarrow \nabla \times \overrightarrow {\bf{B}} = 0\,\,\,\left( {{\text{for }}r > R} \right)$$ is the correct answer to “Consider an infinitely long straight cylindrical conductor of radius R with its axis along the Z-direction, which carries a current of 1A uniformly distributed over its cross-section. Which of the following statements is correct? (where, r is the radial distance from the axis of the cylinder)”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$l{B_0}R{\bf{\hat k}}$$ is the correct answer to “A circular arc QTS is kept in an external magnetic field $${\overrightarrow {\bf{B}} _0}$$ as shown in figure. The arc carries a current $$l$$. The magnetic field is directed normal and into the page. The force acting on the arc is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

-1 is the correct answer to “The trace of a 3 × 3 matrix is 2. Two of its eigen values are 1 and 2. The third eigen value is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$\overrightarrow {\bf{B}} = {\mu _0}K\overrightarrow {\bf{i}} /2$$ is the correct answer to “An infinite conducting sheet in the X-Y-plane carries a surface current density K along the Y-axis. The magnetic field $$\overrightarrow {\bf{B}} $$ for z > 0 is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$R = {\left( {\frac{{n - 1}}{{n + 1}}} \right)^2},\,T = \frac{{4n}}{{{{\left( {n + 1} \right)}^2}}}$$ is the correct answer to “A plane electromagnetic wave of frequency ω is incident normally on an air-dielectric interface. The dielectric is linear, isotropic, non-magnetic and its refractive index is n. The reflectance (R) and transmittance (T) from the interface are”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

increase eight times is the correct answer to “A conducting sphere of radius R has charge +Q on its surface. If the charge on the sphere is doubled and its radius is halved, the energy associated with the electric field will”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$\overrightarrow {\bf{p}} = - qa{\bf{\hat i}} - qa{\bf{\hat j}}$$ is the correct answer to “Four charges are placed at the four corners of a square of side a as shown in the figure. The electric dipole moment of this configuration is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

always independent of frequency is the correct answer to “Far away from any of the resonance frequencies of a medium, the real part of the dielectric permittivity is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$\frac{{{\sigma _0}\pi {a^3}}}{4}{\bf{\hat x}}$$ is the correct answer to “A circular disc of radius a on the XY-plane has a surface charge density $$\sigma = \frac{{{\sigma _0}r\cos \theta }}{a}.$$ The electric dipole moment of this charge distribution is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

The potential difference between any two arbitrary points in the region R is zero is zero is the correct answer to “An electrostatic field $$\overrightarrow {\bf{E}} $$ exists in a given region R. Choose the wrong statement.”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$\frac{{{\mu _0}{J_0}{d^2}}}{3}\hat \phi $$ is the correct answer to “A long cylindrical kept along Z-axis carries a current density $${\bf{\hat J}} = {J_0}r{\bf{\hat k}},$$ where $${J_0}$$ is a constant and r is the radial distance from the axis of the cylinder. The magnetic induction $$\overrightarrow {\bf{B}} $$ inside the conductor at a distance d from the axis of the cylinder is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

along $$ - {\bf{\hat i}}$$ for Z > 0 and along $${\bf{\hat i}}$$ for Z < 0 is the correct answer to “A uniform surface current is flowing in the positive Y-direction over an infinite sheet lying in X-Y plane. The direction of the magnetic field is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$${E_0}\left( {{\bf{\hat x}} + {\bf{\hat y}}} \right)\exp \left[ {i\left( {kz - \omega t} \right)} \right]$$ is the correct answer to “The electric field $$\overrightarrow {\bf{E}} \left( {\overrightarrow {\bf{r}} ,\,t} \right)$$ for a circularly polarized electromagnetic wave propagating along the positive Z-direction is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

linearly polarized at -45° to X-axis is the correct answer to “The stateof polarization of light with the electric field vector $$\overrightarrow {\bf{E}} = {\bf{\hat i}}{E_0}\cos \left( {kz - \omega t} \right) - {\bf{\hat j}}{E_0}\cos \left( {kz - \omega t} \right)$$ is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

not be confined to any plane is the correct answer to “A particle with an initial velocity $${v_0}{\bf{\hat i}}$$ enters a region with an electric field $${E_0}{\bf{\hat j}}$$ and a magnetic field $${B_0}{\bf{\hat j}}.$$ The trajectory of the particle will”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

πr2 αB0 e-αt is the correct answer to “A thin conducting wire is bent into a circular loop of radius r and placed in a time dependent magnetic field of magnetic induction. $$\overrightarrow {\bf{B}} \left( t \right) = {B_0}{e^{ - \alpha t}}{{\bf{\hat e}}_z},\,\,\left( {{B_0} > 0{\text{ and }}\alpha > 0} \right)$$ such that, the plane of the loop is perpendicular to $$\overrightarrow {\bf{B}} \left( t \right).$$ Then the induced emf in the loop is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$\nabla \times \overrightarrow {\bf{E}} = - \frac{{\partial \overrightarrow {\bf{B}} }}{{\partial t}}$$ is the correct answer to “Which one of the following Maxwell's equations implies the absence of magnetic monopoles”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

non-zero inside and zero outside the solenoid is the correct answer to “An infinitely long closely wound solenoid carries a sinusoidally varying current. The induced electric field is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$\overrightarrow {\bf{r}} \times \overrightarrow \nabla \left( {\overrightarrow {\bf{m}} .\overrightarrow {\bf{B}} } \right)$$ is the correct answer to “A magnetic dipole of dipole moment $$\overrightarrow {\bf{m}} $$ is placed in a non-uniform magnetic field $$\overrightarrow {\bf{B}} .$$ If the position vector of the dipole is $$\overrightarrow {\bf{r}} ,$$ the torque acting on the dipole about the origin is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.