Question

why there is no work done in moving charge from one point to another on equipotential surface??

Answer 1

An equipotential surface is one in which all the points are at the same electric potential. If a charge is to be moved between any two points (say from point A to point B) on an equipotential surface, according to the formula dW=q⋅dVdW=q⋅dV, the work done becomes zero.

Answer 2

The expected distinction between any two places of the equipotential surface is zero.

Reason

Potential is characterized to such an extent that it is equivalent to less the work done, and it doesn't change assuming it's an equipotential.

F = qE = - q dV/dx

The power and field are at the right angles to an equipotential surface.

The expected distinction between any two places of the equipotential surface is zero. We have

V1 - V2 = W q Wq = 0 ⇒ W = 0

Therefore, the work done in moving a charge on an equipotential surface is zero.

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