#### Question

"For any charge configuration, equipotential surface through a point is normal to the electric field." Justify.

#### Solution

We know that the work done (*W*) in moving a test charge along an equipotential surface is zero. This is because an equipotential surface is a surface with a constant value of potential

at all the points on the surface.

*∴ W *= *Fs *cos*θ* = 0

Here, F is the electric force and s is the magnitude of displacement of the charge.

For non-zero displacement, this is possible only when cos*θ* is equal to 0.

i.e. cos*θ** = 0*

*⇒θ = 90°*

Thus, the force acting on the point charge is perpendicular to the equipotential surface. We know that the lines of force or the electric field lines indicate the direction of electric force on a charge. Thus, for any charge configuration, equipotential surface through a point is normal to the electric field.