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A positive charge is moved from one point to another point along an equipotential surface. The work required to the move the chargedepends on the sign of the potentialdepends on the magnitude of the potentialis negativeis positiveis zero

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Equipotential surface is defined as the surface where electric potential remains constant

so here voltage is constant

so on equipotential surface we know that


\Delta V = 0

so we know that work done is defined as


W = q\Delta V

now we can say


W = 0

so work done on this surface must be zero

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