Four identical charges q are placed at the corners of a square of side a. Find the potential energy of one of the charges due to the remaining charges.
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Explanation

The electric potential of point A due to the charges placed at B, C and D is
`V=1/(4piepsi_(0))q/a+1/(4pi epsi_(0))q/(sqrt(2)a)+1/(4piepsi_(0))q/a=1/(4pi epsi_(0))(2+1/sqrt(2))q/a`
`:.` Potential energy of the charge at a is `=qV=1/(4piepsi_(0))(2+1/sqrt(2))q^(2)/a`.