Question

Prove using Coulomb's law the path -independence of work done by an electrostate field.

Answer 1

In an electrostatic field, the work done only depends on the final points, and not the path taken. So when in a closed loop the charge returns back to it's original position, the work done is zero. This is because the net potential drop in the path of the charge is zero (since it returns to the same point). Since net potential drop is zero, the net work done on the charge will also be zero because the net potential drop is equal to the net work done divided by the magnitude of the charge in coulombs.

P=W/Q

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