Electric Potential Energy Due to Multiple Charges:
A Numerical Example 
That's all there is to it. Now let's try an example.
These charges are already in place:
How much work is required to bring in an additional charge q? This additional charge q is located at x = 0.2 m, y = 0.1 m. How much work is required to move this charge q in from infinity to this location?
That is, What is the PE of charge q because the other Q's are there?
Find the PE for the new charge q and each other charge Q; then add up the sum (ordinary, scalar addition).
Electric Potential Engergy -- like any form of Potential Energy or any form of Energy or any form of work -- is a scalar. There is do direction associated with work or energy. The sum of the Potential Energy terms involves just an ordinary scalar equation. That's easy; make use of it.
(c) Doug Davis, 2000; all rights reserved
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