Question

(i) Draw the equipotential surfaces corresponding to a uniform electric field in the z-direction.

(ii) Derive an expression for the electric potential at any point along the axial line of an electric dipole.

Answer 1

(i) The equipotential surfaces are as shown in Fig.

(ii) Electric potential on the axial line of an electric dipole.

Let an electric dipole consist of two charges -q and +q separated by a distance 2a as shown in the figure. Let us find electric potential at point P, at a distance r from the mid-point of the dipole.

The electric potential of OP due to the dipole is given b

For a short dipole: r >> a, so r² - a² ≃ r²

So V = \(\frac{1}{4\piɛ_o} \frac{p}{r^2}\)