## Point charges and potential energy and right triangles

domalij
Posts: 3
Joined: Wed Jun 27, 2018 7:04 pm

### Point charges and potential energy and right triangles

Two point charges are located at two of the vertices of a right triangle, as shown in the figure. If a third charge -q is brought from infinity and placed at the third vertex, what will its potential energy be?

They give a figure and values to plug in, and I can give those if you need them, but I was just wanting to know what equation to use. Thanks in advance.

jeff
Posts: 38
Joined: Mon Mar 05, 2018 11:54 pm

### Re: Point charges and potential energy and right triangles

Hi domalij,
domalij wrote:
Wed Jun 27, 2018 7:08 pm
Two point charges are located at two of the vertices of a right triangle, as shown in the figure. If a third charge -q is brought from infinity and placed at the third vertex, what will its potential energy be?

They give a figure and values to plug in, and I can give those if you need them, but I was just wanting to know what equation to use. Thanks in advance.
In this situation, because there are only point charges in the problem, we can use this formula for the potential energy U:

U = k q1 q2 / r

where r is the distance between two point charges. Do you see how to use that for this problem, where they want the potential energy of one particular charge?

domalij
Posts: 3
Joined: Wed Jun 27, 2018 7:04 pm

### Re: Point charges and potential energy and right triangles

But that formula only has two charges. What do I do since there are three charges in the problem?

jeff
Posts: 38
Joined: Mon Mar 05, 2018 11:54 pm

### Re: Point charges and potential energy and right triangles

domalij wrote:
Wed Jun 27, 2018 8:38 pm
But that formula only has two charges. What do I do since there are three charges in the problem?
That formula gives the potential energy for a pair of point charges. So when they ask for the potential energy of a particular point charge, you use that formula multiple times.

For example, in your problem, let's call the original two charges q1 and q2, and the third charge that was moved q3. We want to find the potential energy of q3.

So the PE of q3 would be found from each pair that it is part of, like this:

U = (PE of q3 and q1) + (PE of q3 and q2)
U = (k q1 q3 / r1) + (k q2 q3 / r2)

(There r1 is the distance between q1 and q3, and r2 is the distance between r2 and r3.)

Then you can plug in what you know for q1, q2, q3. So the main idea is that the formula gives the PE of a pair of point charges, and we have to use a term for each pair that we need.

I hope that makes sense! Let me know if you still have questions.

domalij
Posts: 3
Joined: Wed Jun 27, 2018 7:04 pm

### Re: Point charges and potential energy and right triangles

Thank you, I understand now.