Question

Write two properties of equipotential surfaces. Depict equipotential surfaces due to an isolated point charge. Why do the equipotential surfaces get closer as the distance between the equipotential surface and the source charge decreases ?

Answer 1

Properties of equipotential surfaces:
1. The electric potential value is same across the surface.
2. The electric field is directed normal to the equipotential surface at all points.
For an isolated point charge electric potential is given by

$V=\frac{kQ}{r}$
So spheres centered on the charge forms an equipotential surface.
Now, $E=-\frac{dV}{dr}$
$dr=\frac{-dV}{E}$
But dV is constant for an equipotential surface. Therefore,
$dr\propto \frac{1}{E}$
Hence, the equipotential surfaces get closer as the distance between the equipotential surface and the source charge decreases.