Potential Energy of a Charge Configuration

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Calculating the total potential energy of a charge configuration involving multiple charges typically requires summing the potential contributions from each charge. In the example of a 2D square with charges at each corner, there is no shortcut to avoid this summation process. The consensus is that a detailed calculation is necessary, as quick methods do not exist for such configurations. The discussion highlights a frustration with tedious calculations in exams, contrasting with the professor's usual approach. Ultimately, understanding the underlying concepts remains essential despite the workload involved.
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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
 
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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.
 
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.
 

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