# Derive an Expression for the Electric Potential at Any Point Along the Axial Line of an Electric Dipole. - Physics

#### Question

Derivation
Sum

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

#### Solution

Suppose P is a point on the axial position of the dipole.
Length of dipole = 2a
Suppose point P is at the distance 'r' from the center of the dipole.

The potential at a point is V = 1/(4piε_0).Q/r

So, the potential at P due to q is V= 1/(4piε_0).q/(a+r)

Potential at P due to -q is V-q = 1/(4piε_0).(-q)/(a-r)

The total potential at P is V = V_q + V_(-q)

= 1/(4piε_0).q/((a + r)) + 1/(4piε_0).(-q)/((r - a))

= q/(4piε_0)[1/((a + r)) + 1/((a - r))]

V = q/(4piε_0).(2a)/((a^2 - r^2))

Concept: Potential Due to an Electric Dipole
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