## Answer & Solution

**Option C**

51.

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

52.

Consider an electric field $$\overrightarrow {\bf{E}} $$ existing in the interface between a conductor and free space. Then, the electric field E is

53.

If the photon were to have a finite mass, then the Coulomb potential between two stationary charges separated by a distance r would

54.

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

55.

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

56.

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

57.

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

58.

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

59.

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

60.

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