Question

If a unit charge is taken from one part to another part over an equipotential surface, then what is the change in electrostatic potential energy of the charge?

Answer 1

Equipotential surface:

1. It is the surface at constant potential.
2. When bodies are at constant potential then the potential difference will be zero between two-point.

Properties of equipotential surface:

1. An equipotential surface is always perpendicular to the electric field.
2. The intersection between $2$ equipotential surfaces is impossible.
3. The equipotential surfaces for a point charge are spherical shells with concentric radii.
4. The equipotential surfaces for a constant electric field are planes perpendicular to the $\mathrm{x}-$axis.

Calculate the work done in the process.

From the above properties, when we shift a unit positive charge from one point to another on an equipotential surface, the potential at each point remains constant.

So, the amount of work done is,

$\mathrm{W}=\mathrm{q}\left({\mathrm{V}}_{\mathrm{f}}-{\mathrm{V}}_{\mathrm{i}}\right)$

$=\mathrm{q}\left(\mathrm{V}-\mathrm{V}\right)$

$=0\mathrm{J}$

Hence, the work done in the process is zero.