What is the effect of charge and distance on electric potential energy?

[nugget]

Homework Statement

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)

Homework Equations

not sure, something linking distance and charge

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?

 

[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.

 

[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?

 

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

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?

 

[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 U_initial, do i need to work out V at A, B and D before i can calculate qV?

 

[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 U_initial is to multiply the third charge by V at A. Same thing for U_final.

 

[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..