Consider the situation of figure. The work done in taking a point charge from P to A is WA, from P to B is WB and from P to C is WC.


Since electric field is a conservative field and therefore electric force is also a conservative force. Therefore, work done will not depend in the path taken.


As for a conservative force field, work done on a charge does not depend on the path taken by the charge but depends only on the initial and final points. Therefore, in this situation,


i.e. WA = WB = WC


The work done in taking a point charge from P to all the points A, B and C is the same.

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