Why is the electric field always at right angles to the equipotential surface? Explain.

QUESTION:

Why is the electric field always at right angles to the equipotential surface? Explain.

ANSWER:

If the electric field is not normal to the equipotential surface, then there will be an electric field component along the surface of equipotential surface. On a constant potential surface electric field should be zero (E = dV/dr = 0) that means electric field component should be zero. Electric field component E Cos Ɵ will be zero if Ɵ is equal to 90 degrees. That means electric field should be perpendicular to the surface.

(Or)

If the electric field (E)is not normal to the equipotential surface, the work done in moving a charge from one point to the other will not be zero, which is a contradiction, thus the electric field is normal to equipotential surface.