A spherical capacitor is made of concentric conductors of radii a and b (b > a). The total charge on the inner sphere of radius a is Q. (i) Derive an expression for the capacitance C.

If the magnetic moment of proton is 2.793\ \mu_N calculate, giving necessary steps, the radio frequency at which nuclear magnetic resonance occurs in water kept in a uniform magnetic field of 2.4\text{ T}.

A point charge +q is located near the corner of a horizontal and a vertical plate as shown below :

Obtain an expression for the electrostatic potential \phi_P using the image method.

A long wire of radius a carries I amperes of current. The magnetic field surrounding it is given by H_\phi = \dfrac{I}{2\pi\rho} for \rho > a. Obtain expressions for (i) the magnetic energy stored per unit length in the region b \ge \rho \ge a and (ii) the equivalent inductance L per unit length.

The following inputs are given : \begin{align*} T_0 &= 5500\text{ K} && \text{(Sun surface temperature)}, \ R &= 7 \times 10^{10}\text{ cm} && \text{(Sun radius)}, \ r &= 6\cdot 4 \times 10^8\text{ cm} && \text{(Earth radius)}, \ D &= 1\cdot 5 \times 10^{13}\text{ cm} && \text{(Sun--Earth distance)}. \end{align*} Assume that the earth and the sun both absorb all electromagnetic radiations incident on them, and that the earth is at a constant temperature T over the day-night cycle. Calculate T.

Show that when the temperature T of a radiating object is not too different from the surrounding temperature T_0, the object obeys Newton's law of cooling.

A radiation gas of temperature T fills a cavity of volume V. The system expands adiabatically and reversibly to a volume equal to 8V. By what factor does the temperature change?

Consider the L\text{-}C\text{-}R circuit shown below :

\begin{align*} R &= 0\cdot 1\ \Omega \ L &= 1\text{ nH} \ C &= 1\text{ nF} \end{align*} (i) Determine its resonance frequency f_0.

Consider a long, line charge with charge density \rho_l = 10^{-6}\text{ coulomb/m}. Find the force acting on a dust particle carrying -10^{-9}\text{ coulomb}, 1\text{ metre} away from the line charge in free space.

The electric field for a uniform plane wave in free space is given by \vec{E} = (\hat{x} + \hat{y})10 e^{j 10 z}. Determine the corresponding magnetic field vector.