Question

What is meant by equipotential surface? Show that the amount of work done in moving a  test charge along the equipotential surface is zero.

Answer 1

The surface which is the locus of all points which are at the same potential is known as the equipotential surface. No work is required to move a charge from one point to another on the equipotential surface. In other words, any surface with the same electric potential at every point is termed as an equipotential surface.

The work done in moving a charge between two points in an equipotential surface is zero. If a point charge is moved from point VA to VB, in an equipotential surface, then the work done in moving the charge is given by

W = q₀(V_A –V_B)

As V_A – V_B is equal to zero, the total work done is W = 0.