What is an equipotential surface ? Show that the electric field at a point on the surface of a charged conductor or just outside it is perpendicular to the surface ?

Explanation

n equipotential surface is that, electric potential at every point of which is the same.
By definition potential difference between two points = work done in carrying unit + ve test charge from one point to another. As for an equipotential surface potential difference is zero hence no work is to be done in moving a test charge from one point to another of an equipotential surface.
Thus,
`dW = vecE. vec(dr) = E dr cos theta = 0" and it leads to " cos theta or theta = 90^@`
Thus, electric field intensity `vecE` on the surface of a conductor is always perpendicular to the surface.