Question

If potential energy increases as like charges are brought closer together, why wouldn't the work done be negative? I thought work was defined as the negative of the change in potential energy.

Answer 1

Explanation:

Yes, potential energy increases as like charges are brought closer.

And it is also correct that the work done is negative of change in potential energy.

But wait, here there are two entities doing work, one is the electrostatic force and other is the force exerted by the external agent bringing the charges closer, so work done by whom is negative of change in potential energy, so actually, it is the work done by the conservative force, which in this case is the electrostatic force.

If you calculate the work done by the force exerted by the external agent, who brought the charges closer then that work will be positive in the above case.

So it has to be specified work done by whom.