## Answer & Solution

**Option B**

21.

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

22.

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)

(where, r is the radial distance from the axis of the cylinder)

23.

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

24.

The trace of a 3 × 3 matrix is 2. Two of its eigen values are 1 and 2. The third eigen value is

25.

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

26.

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

27.

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

28.

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

29.

Far away from any of the resonance frequencies of a medium, the real part of the dielectric permittivity is

30.

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