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

Explanation

Consider a point P situated at a distance r from mid-point of an electric dipole along its axial line.
Electric potential at P due to +ve charge at B,` V_B = 1/(4pi epsi_0) . q/((r-a))`

and electric potential at P due to - ve charge at A, `V_A = 1/(4pi epsi_0). ((-q))/((r+a))`
`:.` Net electric potential at point P,
`V = V_B + V_A = 1/(4pi epsi_0) . q/((r-a)) - 1/(4pi epsi_0) .q/((r + a))`
`=q/(4 pi epsi_0)[1/((r-a)) - 1/((r + a))] = q/(4pi epsi_0) . (2a)/((r^2 -a^2)) = p/(4pi epsi_0(r^2 - a^2))`
If `r gt gt a`, then we have `V = p/(4pi epsi_0r^2)`.