(i) Obtain the expression for the potential to show due to a point charge. (ii) Potential, due to an electric dipole (length 2a) varies as the ‘inverse square’ of the distance of the ‘field point’ from the centre of the dipole for r > a.

(i) Two isolated metal spheres A and B have radii R and 2R respectively, and same charge q. Find which of the two spheres have greater : (a) capacitance and (b) energy density just outside the surface of the spheres. (ii) (a) Show that the equipotential surfaces are closed together in the regions of strong field and far apart in the regions of weak field. Draw equipotential surfaces for an electric dipole. (b) Concentric equipotential surfaces due to a charged body placed at the centre are shown. Identify the polarity of the charge and draw the electric field lines due to it.

Two point charges q and –q are located at points (0, 0, – a) and (0, 0, a) respectively. (i) Find the electrostatic potential at (0, 0, z) and (x, y, 0). (ii) How much work is done in moving a small test charge from the point (5,0,0) to (– 7, 0, 0) along the x-axis ? (iii) How would your answer change if the path of the test charge between the same points is not along the x-axis but along any other random path ? (iv) If the above point charges are now placed in the same positions in the uniform external electric field $\stackrel{\rightarrow}{E}$ what would be the potential energy of the charge system in its orientation of unstable equilibrium ? Justify your answer in each case.