Question

show mathematically that potential at a point on equatorial line of an electric dipole is zero

Answer 1

Consider an electric dipole consisting of 2 point charges −q

−q

and +q

+q

separated by a distance 2l

2l

. Let p be a point on a perpendicular bisector of a dipole at distance r from center O.

V Q q+ =14π∈ 0 qBQ

VQq+=14π∈0qBQ

V Q q− =14π∈ 0 −qAQ

VQq−=14π∈0−qAQ

$V_Q= V_{P_{q+}}+V_{p_{q-}}

V_Q= \large\frac{q}{4 \pi \in_0} \bigg[ \large\frac{1}{BQ}-\frac{1}{AQ} \bigg]

V_Q=0

BQ=AQ$

The net electrostatic potential at a point in the electric field due to an electric dipole at any point on the equatorial line is zero.

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