Question

What is the shape of equipotential surfaces for an isolated point charge?

Answer 1

Equipotential surface:

1. An equipotential surface is basically a surface where all the points lying on the surface have the same electrical potential.
2. For a single charged particle either positive or negative, electric field lines are radial starting from or ending at the charge for positive and negative charges respectively means electric field lines move radially outward for positive charges and move radially inward for negative change.
3. The component of the electric field parallel to an equipotential surface is zero as the potential does not change in this direction.
4. The electric field$\left(E\right)$ and potential$\left(V\right)$ are related mathematically as $E=-\nabla V$
   Here $\nabla V$ is the gradient of potential
5. Thus, the electric field is perpendicular to the equipotential surface at each point of the surface.

Hence, the shape of an equipotential surface due to a single isolated charge is a concentric sphere.