Question

Explain why, for any charge configuration, the equipotential surface through a point is normal to the electric field at that point. Draw a sketch of equipotential surface due to a single –q charge, depicting the electric field lines due to the charge.

Answer 1

As on equipotential surface work done in moving charge is zero
Let is consider work done in moving charge q from ptA to Pt B,
Wab = Vb - Va
Wab =zero ( as potential is constant) -eq1

Also we know work done can be represented by W=E.dx

as from eq 1 we know work done =0
È.dx=0
È dx cos theta =0

cos theta is 0 only when theta =90degree

Hence electric field lines are perpendicular to equipotential surface