Here’s How to Crack It
In this case, an outside agent must be pushing the charge to make it move because
the electric force naturally pushes negative charges against field lines. Therefore,
we expect that the work done by the electric field is negative. The electric force,
FE = (−q)E, points in the direction opposite to the displacement, so the work it
does is WE = −FEr = −qEr, and the change in electrical potential energy is positive:
∆UE = −WE = −(−qEr) = qEr. Since the change in potential energy is positive, the
potential energy has increased; this always happens when the field does negative
work. It’s like when you lift a rock off the ground: Gravity does negative work, and
the rock gains gravitational potential energy.