''for any charge configuration, equipotential surface through a point is normal to the electric feild.'' justify.
We know that the work done(W) in moving a test charge along an equipotential surface is zero and this is because an equipotential surface is a surface with a constant value of potential at all points on the surface.
where, F = Electric force
s = Magnitude of displacement of the charge
For non-zero displacement this is possible only when , where
Thus, the force acting on the point charge is perpendicular to the equipotential surface.
We also know that the lines of force or the electric field lines indicate the direction of electric force on a charge, therefore, for any charge configuration, euipotential surface through a point is normal to the electric field.