# Confusion with Electric Potential/Potential Energy

1. Feb 22, 2005

### sisigsarap

There is a problem I am finding quite confusing:

Two particles, with charges of 20.0 nC and -20.0nC, are placed at the points with coordinates (0,4.00cm) and (0,-4.00cm). A particle with charge 10.0 nC is lcoated at the origin. Find the electric potential energy of the configuration of the three fixed charges.

I am having difficulty understanding the last sentence. For electric potential energy I thought I would use V = 8.99*10^9(q/r) , where I would sum up each charge? For example:

V1 = 8.99*10^9(20nC/4cm) V2 = 8.99*10^9(-20nC/4cm) V3=8.99*10^9(10/0)

Then the Electric potential energy would be V1 + V2 + V3 = 0?

Or would I use U = 8.99*10^9(q1*q2)/(distance from q1 to q2)

and follow the same procedure?

I am very confused with the question and what the book refers to as potential energy and electrical potential??

Any help is appreciated!

Thanks!

2. Feb 22, 2005

### Andrew Mason

Since the electric potential, V, is the potential energy per unit charge it is a scalar quantity that is a function of the separation and the charge. Since it is directionless, potentials can just be added together.

$$V = U/q = \int_\infty ^R \frac{kQ}{r^2}dr = \frac{kQ}{R} - 0$$

$$U = Vq = \frac{kQq}{R}$$

In order to find the total potential energy, take the potential energy of each pair of charges and add them up (be careful with the signs).

The answer, I think, is -4.5e-5 J.

AM

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