(a) Draw the equipotential surfaces corresponding to a uniform electric field in the z-direction.
(b) Derive an expression for the electric potential at any point along the axial line of an electric dipole

Explanation

Expression for the electric potential at any point along the axial line of electric dipole :

Electrostatic potential at point P due to + q charge
`V_(+_(q))=1/(4piin_(0))(+q)/((r-a))" ...(1)"`
Electrostatic potential at point P due to - q charge
`V_(+_(q))=1/(4piin_(0))(+q)/((r+a))" ...(2)"`
Not potential at point P according to the priclple of superposition
`V-V_(+q)+V_(-q)`
`V=1/(4piin_(0))(+q)/((r-a))+1/(4piin_(0))(-q)/((r+a))`
`V=q/(4piin_(0))[1/(r-a)-1/(r+a)]`
`V=q/(4piin_(0))[(r+a-r+a)/(r^(2)-a^(2))]`
`V=q/(4piin_(0))(2a)/((r^(2)-a^(2)))" Electric dipole moment P = q (2a)"`
`V=1/(4piin_(0))P/(r^(2)-a^(2))`