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Electrostatic Potential And Capacitance

Question

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No work is done in moving test charge over an equipotential surface. Why?

Solution

If, a positive test charge q is moved from point A to B, then,

V_{B} - V_{A} = \frac{W_{AB}}{q}

where, W_AB is work done to move charge q from A to B.
Since, two points A and B are on the same equipotential surface,

V_B-V_A=0

∴ W_{AB} = 0

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