Question
Fri March 06, 2015 By: Kb Aulakh

''for any charge configuration, equipotential surface through a point is normal to the electric feild.'' justify.

Expert Reply
Faiza Lambe
Fri March 06, 2015

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.

begin mathsize 14px style therefore straight W equals Fs space cosθ space equals space 0 end style

where, F = Electric force

            s = Magnitude of displacement of the charge

For non-zero displacement this is possible only when begin mathsize 14px style cos space straight theta space equals 0 end style , where begin mathsize 14px style straight theta equals 90 to the power of straight o end style

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.

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