A hollow metallic sphere has an inner radius $a$, outer radius $b$ and resistivity $\rho$. If a potential difference $V$ is applied between the inner and outer surface. Find the (i) resistance between inner and outer surface (ii) total current
(iii) current density in the function of radial distance $J=f\left(r\right)$
(iv) electric field in the function of radial distance $E=f\left(r\right)$

(a) A steady current flows in a metallic conductor of the non-uniform cross-section. State which of the quantities, i.e., current, current density, electric field, and drift velocity remain constant?

(b) A steady current passes through a cylindrical conductor. Is there an electric field inside the conductor?

A potential difference $V$ is applied to copper wire of diameter $d$ and length $L.$ What will be the effect on the electron drift speed, by doubling:

(a) voltage $V$, 

(b) length $L$ and

(c) diameter $d$

The following table gives the length of three copper rods, their diameters and the potential differences between their ends. Rank the rods according to (a) the magnitude of the electric field within them, (b) the drift speed of electrons through them and (c) the current within them, greatest first.

The $V-I$ graph for a metallic wire at two different temperatures $T_1$ and $T_2$ is shown in the figure. Which of the two temperatures $T_1$ and $T_2$ is higher and why?

A beam contains $2.0\times {10}^8$ doubly charged positive ions per cubic centimetre, all of which are moving towards the north with a speed of $1.0\times {10}^5{ \mathrm{m} \mathrm{s}}^{-1}$. (a) What are the magnitude and direction of the current density $\overrightarrow{J}$?

(b) Can you calculate the total current $i$ in this ion beam? If not, what additional information is needed?