Question

Explain the following statement giving reason:

An equipotential surface through a point is normal to the electric field at that point.

Answer 1

Work done to move a charge q on an equipotential surface is zero (W = q∆V = 0). Since W = `int vec E * d vec l` = Edl cos θ, for W to be zero with non-zero field and displacement, cos θ must be zero. Thus θ = 90°, meaning the field is perpendicular to the surface.