Question

Derive the expression for the electric potential at any
point along the axial line of an electric dipole?

Answer 1

Let P be an axial point at distance r from the center of the dipole. Electric potential at point P is given as

$V=V_1+V_2$

$V_1$and $V_2$are the potentials at point P due to charges +q and –q respectively

$V=\frac{1}{4\pi {\epsilon }_0}(\frac{q}{r-2a}+\left(\frac{-q}{r+2a}\right))$

$V=\frac{1}{4\pi {\epsilon }_0}\left(\frac{4a}{(r^2-4a^2)}\right)$

$V=\frac{1}{4\pi {\epsilon }_0}\left(\frac{2P}{(r^2-4a^2)}\right)$

Hence, the electric potential is $\frac{1}{4\pi {\epsilon }_0}\left(\frac{2P}{(r^2-4a^2)}\right)$