The discussion revolves around the application of Coulomb's law and the concept of potential energy in a system involving two electrons. Participants are examining the derivation of potential energy and the implications of the movement of both charges in relation to their separation distance.
The discussion is ongoing, with participants providing insights into the nuances of the calculations involved. Some guidance has been offered regarding the interpretation of variables and their meanings in the context of the problem, but no consensus has been reached on the correct approach.
Participants are grappling with the definitions of variables such as "dr" and "dx" in the context of their specific problem, indicating potential confusion or misapplication of terms. There is also mention of the initial conditions of the electrons starting from rest and moving to infinity.
I think this is quite instructive. First, imagine that one electron is held in place by an external force. As that electron does not move, the restraining force does no work. The second electron moves off to infinity with the calculation you have done. That electron, therefore, gets all the PE of the system. Once it's far enough away, you could release the first electron and there is no more PE to be squeezed out of the system.laser said:
But does this mean that dr is actually 2dr? Would this not double the potential energy?PeroK said:
If you label the electrons and take ##dx_1## as the differential along the path of one of the electrons, then ##dr = 2dx_1##. If you use that in your calculation, you get half the KE for the first electron. And the same KE for the other.laser said: