Derive the expression for the electric potential due to an electric dipole at a point on its axial line.

Explanation

Electric potential at a point in an electric field of a point charge is defined as the amount of work done in moving a unit positive charge from infinity to that point against the electrostatic forces.
Expression. Let a source charge q be at O and let us find potential at P at a distance r from O. while moving a unit positive test charge from `prop` towards P, let we reach at A at a distance x from O. Force on unit positive charge, `F = 1/(4pi epsi_0) q/x^2`

Small work done in moving unit positve test charge from A to B is :
`dW = vecF.d vecx = Fdx cos 180^@ = -Fdx = - 1/(4pi epsi_0)1/r = 1/(4pi epsi_0) q/r`
This work done is stored in the form of electric potential (V)
`:. V = 1/(4pi epsi_0) q/r`