I was trying to solve this problem yesterday and I was not able to. I looked it up its solution but my mind is not still clear about it. "The work done by an external force to move a -6,5C charge from point A to B is 15J. If the charge was started from the rest and had 4.86J of kinetic energy when it reached point B, what must be the potential difference between A and B?" Solution says "By the work-energy theorem, the total work done, by the external force and the electric field together, is the change in kinetic energy". The rest is just solving the math. Why I don't understand is this external work, what is it exactly? is this a force that literally TAKES that negative charge and PUT it in point B?? I just can't visualize it. Has this external force PUSHED the negative charge from somewhere to point B so that the charge gained potential energy? I assume this negative charged was moved AWAY from the positive charge so that it can gain potential energy? Am I correct? Then what has exactly this external force done?? How is it that we need to ADD two works to get the kinetic energy? I'm so confused. By the way, I'm not posting my homework here, I'm not a student, I'm just trying to understand the concept of electric potential.