(a) (i) Draw equipotential surfaces for an electric dipole.

(ii) Two point charges $q_1$ and $q_2$ are located at $\overrightarrow{r_1}$ and $\vec{r}_2$ respectively in an external electric field $\vec{E}$. Obtain an expression for the potential energy of the system.

(iii) The dipole moment of a molecule is $10^{-30} \mathrm{Cm}$. It is placed in an electric field $\vec{E}$ of $10^5 \mathrm{~V} / \mathrm{m}$ such that its axis is along the electric field. The direction of $\vec{E}$ is suddenly changed by $60^{\circ}$ at an instant. Find the change in the potential energy of the dipole, at that instant.

OR

(b) (i) A thin spherical shell of radius R has a uniform surface charge density $\sigma$. Using Gauss' law, deduce an expression for electric field (i) outside and (ii) inside the shell.

(ii) Two long straight thin wires AB and CD have linear charge densities $10 \mu \mathrm{C} / \mathrm{m}$ and $-20 \mu \mathrm{C} / \mathrm{m}$, respectively. They are kept parallel to each other at a distance 1 m . Find magnitude and direction of the net electric field at a point midway between them.

(a) (i) Use Gauss' law to obtain an expression for the electric field due to an infinitely long thin straight wire with uniform linear charge density $$\lambda$$.

(ii) An infinitely long positively charged straight wire has a linear charge density $$\lambda$$. An electron is revolving in a circle with a constant speed $$v$$ such that the wire passes through the centre, and is perpendicular to the plane, of the circle. Find the kinetic energy of the electron in terms of magnitudes of its charge and linear charge density $$\lambda$$ on the wire.

(iii) Draw a graph of kinetic energy as a function of linear charge density $$\lambda$$.

OR

(b) (i) Consider two identical point charges located at points $$(0,0)$$ and $$(a, 0)$$.

(1) Is there a point on the line joining them at which the electric field is zero?

(2) Is there a point on the line joining them at which the electric potential is zero?

Justify your answers for each case.

(ii) State the significance of negative value of electrostatic potential energy of a system of charges.

Three charges are placed at the corners of an equilateral triangle $$A B C$$ of side $$2.0 \mathrm{~m}$$ as shown in figure. Calculate the electric potential energy of the system of three charges.