I know that they repel but I don't get the work done and energy conversion

Question

Two positive charges are brought closer together. Describe the work done and the energy conversion that occurs.

Answer 1

One must do positive work to bring to charges of the same sign together since they repel each other (the force applied is in the same direction as the displacement of the charge). On the right side, e.g., the repulsive force is to the right, but the applied force must be to the left and the displacement must also be to the left. A similar statement applies for the left side.

 

The work done is converted into potential energy. If one were to let the charges go after moving them closer, the potential energy would change into kinetic energy.

Answer 2

Another way to look at it is, basically, any time you force something to go a way it does not naturally want to go, you have to do positive work on it.  And any time you do positive work against a conservative force, like gravity or the electric force or the magnetic force, you store that positive work as potential energy (for example, lifting up a book; under the (conservative) force of gravity, that moves the book a way it does not naturally want to go, so you do positive work on it to lift it, and that work is stored as potential energy).

 

Moving two like charges together is moving them a way they do not naturally want to go, in a conservative situation.  So you have to do positive work, and it is stored as potential energy.

 

If an object is moving the way it naturally wants to go, and you are slowing down that motion, you conversely have to do negative work, and potential energy is lost.

 

(You can also explain this in terms of work done by the conservative force itself, using the conservation of mechanical energy expression, to show that the work done BY the conservative force relates exactly to negative the change in potential energy; so as the conservative force does positive work -- meaning the object is moving the way it naturally wants to go -- the object loses potential energy).