Question

(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.

Answer 1

a) Equipotential surfaces to an electric field in z direction are all the planes parallel to XY plane

This is because equipotential surfaces are always perpendicular to the electric field. the planes perpendicular to the electric field here are all the planes parallel to XY plane.

b) The electric field due to a dipole on the axial line is given by the formula derived in the picture

- you can see that , if the point P is far away i.e., r >> l, then

we can reduce the expression to ( 2.K.q.l )  / r^3

where q.l is defined as the electric dipole moment of the dipole of length l