In order to plot the equipotential lines for an electric dipole, we observe that for a given Q and d, a constant V requires that is a constant. From this we can write to be the equation for an equipotential surface and a family of surfaces can be generated for various values of c_v.When plotted in 2-D this would give equipotential lines.

To determine the equation for the electric field lines, we note that field lines represent the direction of in space. Therefore,

, k is a constant .................................................................(2.48)

.................(2.49)

For the dipole under consideration =0 , and therefore we can write,

.........................................................(2.50)