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)/(4 pi epsilon_0)q/a + (1)/(4 pi epsilon_0)q/(sqrt(2 a)) = (1)/(4 pi epsilon _0)q/a = (1)/(4 pi epsilon _0)(2 + (1)/(sqrt(2)))q/a`
Therefore, potential energy of the charge at A is
`q V = (1)/(4 pi epsilon_0) (2 + (1)/(sqrt(2)))(q^2)/a`.