Electromagnetic Theory — Part 2 MCQs with Explanations

-5πr2L2 is the correct answer to “A cylindrical rod of length L and radius r, made of an inhomogeneous dielectric, is placed with its axis along the Z-direction with one end at the origin as shown below. If the rod carries a polarization $$\overrightarrow {\bf{P}} = \left( {5{z^2} + 7} \right){\bf{\hat k}},$$ the volume bound charge inside the dielectric is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

28.05 nF is the correct answer to “A coaxial cable of uniform cross-section contains an insulating material of dielectric constant. The radius of the central wire is 0.01 m and that of the sheath is 0.02 m. The capacitance per kilometre of a cable is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

Radially outward $$\left( {{\bf{\hat r}}} \right)$$ is the correct answer to “A parallel plate capacitor is being discharged. What is the direction of the energy flow in terms of the Poynting vector in the space between the plates”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

The force on Q2 is the same in magnitude as that on Q1 is the correct answer to “Two point charges Q 1 = 1 nC and Q 2 = 2 nC are kept in free space such that the distance between them is 0.1 m. Which of the statements is correct”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$\frac{{800}}{\pi }$$ is the correct answer to “The magnetic field (in A/m) inside a long solid cylindrical conductor of radius a = 0.1 m is $$\overrightarrow {\bf{H}} = \frac{{{{10}^4}}}{r}\left[ {\frac{1}{{{\alpha ^2}}}\sin \left( {\alpha r} \right) - \frac{r}{\alpha }\cos \left( {\alpha r} \right)} \right]\hat \phi ,$$ where, $$\alpha = \frac{\pi }{{2a}}.$$ What is the total current (in ampere) in the conductor”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

there is no torque about the centre at O on the dipole is the correct answer to “Four point charges are placed at the corners of a square whose centre is at the origin of a Cartesian coordinate system. A point dipole $$\overrightarrow {\bf{p}} $$ is placed at the centre of the square as shown in the figure. Then,”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$${E_{0r}} = - \frac{2}{5}V/m,\,{E_{0t}} = \frac{8}{5}V/m$$ is the correct answer to “A plane electromagnetic wave travelling in vacuum is incident normally on a non-magnetic, non-absorbing medium of refractive index n. The incident (E i ), reflected (E r ) and transmitted (E t ) electric fields are given as E i = E exp[i(kz - ωt)], E r = E 0r exp[i(k r z - ωt)], E t = E 0t exp[i(k t z - ωt)] If E = 2 V/m and n = 1.5, then the application of appropriate boundary conditions leads to”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

zero is the correct answer to “An electric field applied along the length of a long, cylinder produces a polarization P. The depolarization field produced in this configuration is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

The electric flux crossing the closed surface S is independent of q2 is the correct answer to “Consider a set of two stationary point charges q 1 and q 2 as shown in the figure. Which of the following statements is correct”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$\frac{{\pi c}}{W}$$ is the correct answer to “Electromagnetic waves are propagating along a hollow, metallic waveguide whose cross-section is a square of side W. The minimum frequency of the electromagnetic waves is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

external to the conductor and normal to the conductor's surface is the correct answer to “Consider an electric field $$\overrightarrow {\bf{E}} $$ existing in the interface between a conductor and free space. Then, the electric field E is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

be strlctly zero beyond some distance is the correct answer to “If the photon were to have a finite mass, then the Coulomb potential between two stationary charges separated by a distance r would”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

zero is the correct answer to “Three infinitely long wires are placed equally apart on the circumference of a circle of radius a perpendicular to its plane. Two of the wires carry current $$l$$ each, in the same direction, while the third carries current 2$$l$$ along the direction opposite to the other two. The magnitude of the magnetic induction $$\overrightarrow {\bf{B}} $$ at a distancer from the centre of the circle for r > a, is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

an integer near $$\frac{\omega }{{2\pi }}$$ and is independent of δ is the correct answer to “A plane electromagnetic wave is given by $${E_0}\left( {{\bf{\hat x}} + {e^{i\delta }}{\bf{\hat y}}} \right)\exp \left\{ {i\left( {kz - \omega t} \right)} \right\}.$$ At a given location, the number of times $$\overrightarrow {\bf{E}} $$ vanishes in 1s is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$\overrightarrow {\bf{B}} = \frac{1}{c}\cos \left( {\omega t - kz} \right){\bf{\hat j}}$$ is the correct answer to “An electromagnetic wave is propagating in free space in the Z-direction. If the electric field is given by $$E = \cos \left( {\omega t - kz} \right){\bf{\hat i}},$$ where $$\omega t = ck,$$ then the magnetic field is given by”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

zero is the correct answer to “The value of $$\int\limits_C {\overrightarrow {\bf{A}} .d\overrightarrow {\bf{l}} } $$ along a square loop of side L in a uniform field $$\overrightarrow {\bf{A}} $$ is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$3{\bf{\hat k}}$$ is the correct answer to “The vector potential in a region is, given as $$\overrightarrow {\bf{A}} \left( {x,\,y,\,z} \right) = - y{\bf{\hat i}} + 2x{\bf{\hat j}}.$$ The associated magnetic induction is $$\overrightarrow {\bf{B}} $$ is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

plane polarized and circularly polarized, respectively is the correct answer to “A classical charged particle moving with frequency ω in a circular orbit of radius a, centred at the origin in the XV-plane, electromagnetic radiation. At points (b, 0, 0) and (0, 0, b), where b ≫ a, the electromagnetic waves are”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$ - \frac{q}{2}{\text{ and }}\frac{R}{2}$$ is the correct answer to “A charge +q is kept at a distance of 2R from the centre of a grounded conducting sphere of radius R. The image charge and its distance from the centre respectively, are”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

30 μm is the correct answer to “A left circularly polarized light beam of wavelength 600 nm is incident on a crystal of thickness d and propagates perpendicular to its optic axis. The ordinary and extraordinary refractive indices of the crystal are n o = 1.54 and n e and = 1.55 respectively. The emergent light will be right circularly polarized, if d is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$\frac{{{d^2}{\mu _x}}}{{d{t^2}}} + {\gamma ^2}B_0^2{\mu _x} = 0$$ is the correct answer to “An atom with net magnetic moment $$\overrightarrow \mu $$ and net angular momentum $$\overrightarrow {\bf{L}} \left( {\overrightarrow \mu = \gamma \overrightarrow {\bf{L}} } \right)$$ is kept in a uniform magnetic induction $$\overrightarrow {\bf{B}} = {B_0}{\bf{\hat k}}.$$ The magnetic moment $$\overrightarrow \mu \left( { = {\mu _x}} \right)$$ is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

repelled towards the lower field because it is diamagnetic is the correct answer to “When liquid oxygen is poured down close to a strong bar magnet, the oxygen stream is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$ - \frac{{{q^2}}}{{4\pi {\varepsilon _0}\left( {4d} \right)}}$$ is the correct answer to “The work done in bringing a charge +q from infinity in free space, to a position at a distance d in front of a semiinfinite grounded metal surface is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$\overrightarrow {\bf{J}} {\text{ along }}\hat \phi ;\overrightarrow {\bf{A}} {\text{ along }}\hat \phi ;\left| {\overrightarrow {\bf{A}} } \right| \propto \frac{1}{d}$$ is the correct answer to “A rod of length L with uniform charge density $$\lambda $$ per unit length is in the XY-plane and rotating about Z-axis passing through one of its edge with an angular velocity $$\overrightarrow \omega $$ as shown in the figure below. $$\left( {{\bf{\hat r}},\,\hat \phi ,\,{\bf{\hat z}}} \right)$$ refer to the unit vectors at Q, $$\overrightarrow {\bf{A}} $$ is the vector potential at a distance d from the origin O along Z-axis for d ≪ L and $$\overrightarrow {\bf{J}} $$ is the current density due to the motion of the rod. Which one of the following statements is correct”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

P-2, Q-4, R-1, S-3 is the correct answer to “Match the following: List-I List-II P. Rest mass 1. Timelike vector Q. Charge 2. Lorentz invariant R. Four-momentum 3. Tensor of rank 2 S. Electromagnetic field 4. Conserved and Lorentz invariant”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

7.4 × 10-5 m/s is the correct answer to “A copper wire of uniform cross-sectional area 1.0 × 0 -6 m 2 carries a current of 1 A. Assuming that each copper atom contributes one electron to the electron gas, the drift velocity of the free electrons (density of copper is 8.94 × 10 3 kg/m 3 and its atomic mass is 1.05 × 10 -25 kg) is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

the point charge is moving with velocity close to that of light is the correct answer to “The electromagnetic field due to a point charge must be described by Lienard Weichert potentials, when”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

quadrupole moment is the correct answer to “Four point charges are placed in a plane at the following positions +Q at (1, 0), -Q at (-1, 0), + Q at (0, 1) and -Q at (0, -1). At large distances the electrostatic potential due to this charge distribution will be dominated by the”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

4qa$${\bf{\hat k}}$$ is the correct answer to “Three point charges q, q and -2q are located at (0, -a, a), (0, a, a) and (0, 0, -a), respectively. The net dipole moment of this charge distribution is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

PA = 0, PB = PC is the correct answer to “Consider the following three independent cases: i. Particle A of charge +q moves in free space with a constant velocity $$\overrightarrow {\bf{v}} $$ (v ≪ speed of light). ii. Particle B of charge +q moves in free space in a circle of radius R with same speed v as In case i. iii. Particle C having charge -q moves as in case ii. If the powers radiated by A, B and C are P A , P B and P C respectively then”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$\frac{{{\mu _0}}}{{2\pi }} \cdot \frac{{a{I_0}\omega }}{R}\ln 2$$ is the correct answer to “An infinitely long wire carrying a current $$I\left( t \right) = {I_0}\cos \left( {\omega t} \right)$$ is placed at a distance a from a square loop of side a as shown in the figure. If the resistance of the loop is R, then the amplitude of the induced current in the loop is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

lags the current in the large coil by $$\frac{\pi }{2}$$ is the correct answer to “A large circular coil of N turns and radius R carries a time varying current $$I = {I_0}\sin \left( {\omega t} \right).$$ A small circular coil of n turns and radius r(r ≪ R) is placed at the centre of the large coil such that the coils are concentric and coplanar. The induced emf in the small coil”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$ - \int\limits_S {\frac{{\partial \overrightarrow {\bf{B}} }}{{\partial t}}.d\overrightarrow {\bf{S}} } + \oint\limits_L {\left( {\overrightarrow {\bf{v}} \times \overrightarrow {\bf{B}} } \right).d\overrightarrow {\bf{L}} } $$ is the correct answer to “A conducting loop L of surface area S is moving with a velocity $$\overrightarrow {\bf{v}} $$ in a magnetic field $$\overrightarrow {\bf{B}} \left( {\overrightarrow {\bf{r}} ,\,t} \right) = {B_0}{t^2},\,{B_0}$$ is a positive constant of suitable dimensions. The emf induced V emf in the loop is given by”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

perpendicular to the plane of incidence and θi = 56° is the correct answer to “Unpolarized light falls from air to a planar air-glass interface (refractive index of glass is 1.5) and the reflected light is observed to be plane polarized. The polarization vector and the angle of incidence θ i are”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

R and S is the correct answer to “Consider the given statements about E(r, t) and B(r, t), the electric and magnetic vectors respectively in a region of free space P. Both E and B are conservative vector fields. Q. Both E and B are central force fields. R. E and B are mutually perpendicular in the region. S. Work done by B on a moving charge in the region is zero. Choose the right combination of correct statements from the following.”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

The group velocity is less than the phase velocity is the correct answer to “Given a wave with the dispersion relation, ω = ck + m for k > 0 and m > 0, which one of the following is true”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

d-2 is the correct answer to “An insulating sphere of radius a carries a charge density $$\rho \left( {\overrightarrow {\bf{r}} } \right) = {\rho _0}\left( {{a^2} - {r^2}} \right)\cos \theta ;\,r < a.$$ The leading order term for the electric field at a distance d, far away from the charge distribution, is proportional to”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$\frac{{\tan {\theta _1}}}{{\tan {\theta _2}}}$$ is the correct answer to “At the interface between two linear dielectrics (with dielectric constants $${{\varepsilon _1}}$$ and $${{\varepsilon _2}}$$), the electric field lines bend, as shown in the figure. Assume that there are no free charges at the interface. The ratio $$\frac{{{\varepsilon _1}}}{{{\varepsilon _2}}}$$ is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

16$${I_0}$$ and $${I_0}$$ is the correct answer to “In a two beam interference pattern, the maximum and minimum intensity values are found to be 25$${I_0}$$ and 9$${I_0}$$ respectively, where $${I_0}$$ is a constant. The intensities of the two interfering beams are”. This question is standard in competitive examination syllabi for Electromagnetic Theory.

$$\frac{1}{{4\pi {\varepsilon _0}}}\frac{{7{q^2}}}{2}$$ is the correct answer to “Two charges q and 2q are placed along the X-axis in front of a grounded, infinite conducting plane, as shown in the figure. They are located respectively at a distance of 0.5 m and 1.5 m from the plane. The force acting on the charge q is”. This question is standard in competitive examination syllabi for Electromagnetic Theory.