Potential Energy of a Charge Configuration

[CogitoEAS]

Is there a quick way to figure out the total potential energy between more than 2 charges without having to find the potential at each point and the. Multiplying it by the charge at that point and adding it all up?

For example - a 2D square with a charges Q, 2Q, -3Q, and another Q at each corner and let's say each side of the square has length "d"

I'm basically wondering if there's a way to calculate the total potential energy of this charge configuration without a page and a half of work

 

[ZetaOfThree]

There really isn't a "quick" way that I know of. You pretty much have to do a sum when calculating the potential energy. That's just the way it's done.

 

[CogitoEAS]

Thank you -I figured as much. I just have a professor who typically writes problems that aren't very tedious especially when you understand the concept(s). I saw a problem like this on an old exam and thought the busywork I had to do was a little uncharacteristic of his testing style.

Thanks again.