Question

Prove that potential at point on transverse (equatorial) position of electric dipole is zero.

Answer 1

Let AB be an electric dipole consisting of +q nd -q charges separated by distance of 2$l$. A point P lies on the neutral axis (or equatorial or transverse position) at a distance r from the centre O of dipole, where we have to determine the potential:
$AP=BP=\sqrt{l^2+r^2}$
Potential at P due to +q charge will be
$V_1=\frac{1}{4\pi \epsilon k}\times \frac{q}{AP}=\frac{q}{4\pi {\epsilon }_{0}k\sqrt{l^2+r^2}}$
Similarly, potential at P due -q charge will be:
$v_2=\frac{1}{4\pi {\epsilon }_{0}k}\left[\frac{-q}{BP}\right]=\frac{-q}{4\pi {\epsilon }_{0}k\sqrt{l^2+l^2}}$
Where k = dielectric constant of medium.
Hence resultant potential at point P,
$V=V_1+V_2$
$V=0$