MIT 8.02 Electricity and Magnetism. Say that we have one positive charge Q alone in space, we bring another positive charge towards it to say point P, then the first charge on its own requires no work to be done to bring it there whereas the second charge does. I am struggling conceptually with the idea of "potential" in connection with the first charge in its own, although we can use formulae to determine the potential at a distance r from the first charge I do not see how this has any physical meaning. Please help.

Question

MIT 8.02 Electricity and Magnetism.  Say that we have one positive charge Q alone in space, we bring another positive charge towards it to say point P, then the first charge on its own requires no work to be done to bring it there whereas the second charge does.  I am struggling conceptually with the idea of "potential" in connection with the first charge in its own, although we can use formulae to determine the potential at a distance r from the first charge I do not see how this has any physical meaning.  Please help.

anonymous · Answer

Before I close my own question I thought best to post the answer I have arrived at.  In looking more closely at the mathematics it's obvious that without more than one charge "potential" has no physical meaning,  this makes perfect sense because the first charge can move around without any resistive force due to other charges and therefore no work is required to move the charge. The potential at a distance from a single point charge is therefore only useful when we introduce more charges into the system and the system gathers potential energy.  The key point is that potential difference is physically meaningful because it expresses the work required to move a charge from one point to another, on its own however "potential" has no physical meaning.  Feel free to correct my answer.  Thanks.

kainui · Answer

Looks good to me! You'll see why voltage is important soon enough I think.