Question

Derive an expression for electric potential at a point due to electric dipole. Hence find its value on (i) axial line and (ii) equatorial line.

Or

Derive an expression for the electric potential at a point along the axial line of an electric dipole.

Answer 1

Let us calculate the electric potential at any point P due to an electric dipole, consisting of two charges -q and +q at A and B respectively separated from each other by a distance 2a from each other. Let 'r' be the distance of the point P from the center O of the dipole and r₁ and r₂ be the distances of P from the centers of charges +q and -q respectively.

....(i)

In ∆OBP,

r₁ = BP = MP = OP - OM

= r - a cos θ

In ∆ANP,

r₂ = PN = NO + OP = OP + NO

= r + a cos θ

So Eq. (i) becomes

(ii) At equatorial line,

θ = 90°

V = \(\frac{pcos90^\circ}{r^2}\) = 0