An equipotential surface is everywhere perpendicular to the electric field that it characterizes. The work done by the electric field on a particle when it is moved from one point on an equipotential surface to another point on the same equipotential surface is always zero.

Why no work is done on equipotential surface?

Answer: An equipotential surface is one in which all the points are at the same electric potential. If a charge is to be moved between any two points (say from point A to point B) on an equipotential surface, according to the formula dW=q⋅dVdW=q⋅dV, the work done becomes zero.

Why no work is done to move a charge on equipotential surface?

Then how a charge could be moved in an equipotential surface without applying any force ? If the force is everywhere perpendicular to the direction of motion then →F⋅d→r=0 so no work is done. Now, the electric field and thus the electric force is precisely everywhere perpendicular to an equipotential, hence q→E⋅d→r=0.