Electromagnetic Theory MCQs Question and Answer in Engineering Physics Page-8 section-1

71.
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

A. 4qa$${\bf{\hat k}}$$

B. 2qa$${\bf{\hat k}}$$

C. -4qa$${\bf{\hat i}}$$

D. -2qa$${\bf{\hat j}}$$

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72.
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

A. P_A = 0, P_B > P_C

B. P_A = 0, P_B = P_C

C. P_A > P_B > P_C

D. P_A = P_B = P_C

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73.
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

A. $$\frac{{{\mu _0}}}{{2\pi }} \cdot \frac{{a{I_0}\omega }}{R}\ln 2$$

B. $$\frac{{{\mu _0}}}{\pi } \cdot \frac{{a{I_0}\omega }}{R}\ln 2$$

C. $$\frac{{2{\mu _0}}}{\pi } \cdot \frac{{a{I_0}\omega }}{R}\ln 2$$

D. $$\frac{{{\mu _0}}}{{2\pi }} \cdot \frac{{a{I_0}\omega }}{R}$$

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74.
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

A. leads the current in the large coil by $$\frac{\pi }{2}$$

B. lags the current in the large coil by $$\pi $$

C. is in phase with the current in the large coil

D. lags the current in the large coil by $$\frac{\pi }{2}$$

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75.
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

A. $$ - \int\limits_S {\frac{{\partial \overrightarrow {\bf{B}} }}{{\partial t}}.d\overrightarrow {\bf{S}} } $$

B. $$\oint\limits_L {\left( {\overrightarrow {\bf{v}} \times \overrightarrow {\bf{B}} } \right).d\overrightarrow {\bf{L}} } $$

C. $$ - \int\limits_S {\frac{{\partial \overrightarrow {\bf{B}} }}{{\partial t}}.d\overrightarrow {\bf{S}} } - \oint\limits_L {\left( {\overrightarrow {\bf{v}} \times \overrightarrow {\bf{B}} } \right).d\overrightarrow {\bf{L}} } $$

D. $$ - \int\limits_S {\frac{{\partial \overrightarrow {\bf{B}} }}{{\partial t}}.d\overrightarrow {\bf{S}} } + \oint\limits_L {\left( {\overrightarrow {\bf{v}} \times \overrightarrow {\bf{B}} } \right).d\overrightarrow {\bf{L}} } $$

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76.
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

A. perpendicular to the plane of incidence and θ_i = 42°

B. parallel to the plane of incidence and θ_i = 56°

C. perpendicular to the plane of incidence and θ_i = 56°

D. parallel to the plane of incidence and θ_i = 42°

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77.
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.

A. P and R

B. R and S

C. S only

D. P and Q

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78.
Given a wave with the dispersion relation, ω = ck + m for k > 0 and m > 0, which one of the following is true?

A. The group velocity is greater than the phase velocity

B. The group velocity is less than the phase velocity

C. The group velocity and the phase velocity are equal

D. There is no definite relation between the group velocity and the phase velocity

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79.
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

A. d^-1

B. d^-2

C. d^-3

D. d^-4

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80.
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

A. $$\frac{{\tan {\theta _1}}}{{\tan {\theta _2}}}$$

B. $$\frac{{\cos {\theta _1}}}{{\cos {\theta _2}}}$$

C. $$\frac{{\sin {\theta _1}}}{{\sin {\theta _2}}}$$

D. $$\frac{{\cot {\theta _1}}}{{\cot {\theta _2}}}$$

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Electromagnetic Theory MCQs Question and Answer in Engineering Physics

71. 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

Answer & Solution

Answer & Solution

73. 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

Answer & Solution

Answer & Solution

Answer & Solution

76. 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 θi are

Answer & Solution

Answer & Solution

78. Given a wave with the dispersion relation, ω = ck + m for k > 0 and m > 0, which one of the following is true?

Answer & Solution

79. 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

Answer & Solution

Answer & Solution

71.
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

73.
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

76.
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

78.
Given a wave with the dispersion relation, ω = ck + m for k > 0 and m > 0, which one of the following is true?

79.
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