# Electric Potential Energy

1. Aug 14, 2009

### nugget

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

A, B, C and D are corners of a square in empty space, sides 12 micrometres, charges +5nC and -5nC are placed at corners A and B respectively.

What is the change in the electric potential from D to C? (take care with sign)

A third charge of -2nC is initially at D then moved to C, what is the change in the potential energy of the system? (take care with sign)

2. Relevant equations

not sure, something linking distance and charge

3. The attempt at a solution

if the charges are in space, there is no conduction of charge so at D and C wouldn't you expect there to be no electric potential?

2. Aug 14, 2009

### kuruman

Please look up in your textbook the equation for the "electric potential due to a point charge". That equation is very relevant as a starting point for this problem.

3. Aug 16, 2009

### nugget

I think i have figured out the first answer;

I got + 2.2x106 Volts for the difference between D and C. I'm not sure if this number is way too large but I wouldn't be surprised seeing as charges were given in nanocoulombs and distances are in micrometers.

now I am unsure what the second half of the question is asking - when it says 'change in potential energy of the system,' does that mean i should put a test charge in the centre and then add the third charge, measure potential, then move the third charge and measure again?

4. Aug 16, 2009

### kuruman

I checked your number and it is correct assuming that points A and C are diagonally across from each other.

For the next part what you are asked to do is

1. Calculate the total potential energy Uinitial with the first two charges where they are and the third charge at point D.
2. Calculate the total potential energy Ufinal with the first two charges where they are and the third charge at point C.
3. Calculate the difference Ufinal - Uinitial

This seemingly three-step problem can be done in one step (and that's the point of this part) if you remember that the potential energy of a charge q is U = q V, where V is the electrostatic potential at the location of the charge.

Can you put it together now?

5. Aug 16, 2009

### nugget

unfortunately A and C are not diagonally opposite, but rather A is top left, B top right and C is bottom left, i.e. D bottom right. is my answer still correct?

When you say calculate Uinitial, do i need to work out V at A, B and D before i can calculate qV?

6. Aug 16, 2009

### kuruman

You have already calculated V at A and V at B in the first part. That is why you can do it in one step. All you need to do to find Uinitial is to multiply the third charge by V at A. Same thing for Ufinal.

7. Aug 16, 2009

### pgardn

you would have a new distance I believe. B would be further away from C than what was given... hypot of a right triangle (root 2 multiplied by what was given...) If I am seeing this correctly

whoops it may not matter based on what was asked..