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

Explanation

Let an electric dipole consists 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 P due to the dipole is given by
`V=(1)/(4piepsi_(0))[(q)/(BP)+((-q))/(AP)]`
`=(q)/(4piepsi_(0))[(1)/(BP)-(1)/(AP)]`
`=(q)/(4piepsi_(0))[(1)/(r-a)-(1)/(r+a)]`
`=(q)(4piepsi_(0))[(r+a-r+a)/(r^(2)-a^(2))]`
`=(1)/(4piepsi_(0))(q2a)/(r^(2)-a^(2))=(1)/(4piepsi_(0))(p)/((r^(2)-a^(2)))" "[becausep=q2a]`.