Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A ball with a charge of is carried slowly by an outside agent from a point A at V to a point B at V. (a) How much work does the agent do? (b) The ball is then released at B and moves back to A. What kinetic energy does it have at A? (c) A ball with a charge of is carried from A to B in the same way. How much work does the agent do?
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. , V, V.
Step 1. The work on the positive ball. . So , that is mJ.
Step 2. The release. The ball moves from B to A, from high to low potential. The potential energy falls by mJ, and the kinetic energy rises by the same amount. It starts from rest, so it has mJ at A.
Step 3. The negative ball. , that is mJ.
Answer: mJ, mJ and mJ.
Check. The negative sign in step 3 says that the field itself does the work, mJ. A negative charge falls towards higher potential, so it does not need to be pushed.
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The work to carry a charge slowly from A to B is , and the potential energy is . Between large plates . A charge that falls through a potential difference gains the kinetic energy , so . .
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