# Distinction between potential energy and electrical potential

1. Jan 27, 2008

### alpha-libri

1. The problem statement, all variables and given/known data

This is a qualitative question, so a numerical solution isn't required at any point. It should be easy, I guess, but I'm hanging up at the end.

There are three large parallel plates A, B, and C with charges per unit area as follows:
A: -8*10^-9C/m^2
B: -8*10^-9C/m^2 (same as A)
C: -2*10^-9C/m^2

Point X is located between A and B, Point Y is located between B and C, as shown. (The dots are space-holders, needed to make the figure look approximately right.)

.....|..X..|..Y..|...
.....A.....B.....C...

The questions are:
(1) Which point has the higher potential energy for an electron? (Explain.)
(2) Which point has the higher electrical potential for an electron? (Explain.)

2. Relevant equations
I can solve for field strength in terms of sigma and epsilon, but that's not really required. The force imposed on an electron by a plate is proportional to the charge density on the plate, and doesn't vary with distance if the plates are "large." The forces are additive, with signs that depend upon the location of the test point.

3. The attempt at a solution

An electron at X experiences (1) a force to the right due to A, (2) to the left due to B, and (3) to the left due to C. Since (1) and (2) cancel out, the only remaining force is due to the -2*10^-9C/m^2 charge density on C, and it's to the left.

On the other hand (or side), an electron at Y experiences (1) a force to the right due to A, (2) a force to the right due to B, and (3) a force to the left due to C. The forces (1) and (2) are in the same direction, opposed by (3), so the net force is produced by the net effective charge density on A and B, which is -14*10^-9C/m^2 . The force is to the right.

That would seem to answer question a. Point Y has the higher potential energy. But what about part b of the question? I may be missing something fundamental, but it seems to me that electrical potential gives rise to the potential energy. So why shouldn't the answer to part b also be, point Y? Or is it???
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution