Question

for any charge configiration,equipotential surface through a point is normal to the electric field?why

Answer 1

if E was not normal to the surface, it would hae some non zero component along the surface.Free charge on the surface of the conductor would then experience force and move. In the static situation , therefore , E should have no tangential component

Answer 2

Hey !!

If the electric field were not normal to the surface, then it would have a component along the surface which would cause work to be done in moving a charge on an equipotential surface.

DETAILED EXPLANATION

Equipotential lines are curved lines with similar altitude that pertains to electric potential or voltage. These lines are always perpendicular to electric field which creates equipotential surfaces in three dimensions. The movement along equipotential surface requires no work as movement is perpendicular to electric field.

As work done in moving test charge along equipotential surface is zero, there appear fixed potential values across every point on equipotential surface so,

           W = Fcosθ = 0

where,

                     F = Electric force

s = Magnitude of displacement of charge

In case, of non-zero displacement, it exists only when

             cos θ = 0

                    θ = 90°

Hence, force acting on point charge is perpendicular to equipotential surface.

Good luck !!