Question

Deduce an expression for electric potential due to an electric dipole at any point on its axis. Mention one contrasting feature of electric potential of dipole at a point as compared to that due to a single charge.

Answer 1

For electric on the axial line,

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 by

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

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

So for a dipole

V ∝ \(\frac{1}{r^2}\)

And for a monopole (or a single charge)

V ∝ \(\frac{1}{r}\).