physic 難題 42

I suppose P and Q are two charges.

Hence, U = kP.Q/(2l)
where k is the electrostatic constant, equals to 9x10^9 N.m^2/C^2
i.e. 2U = kPQ/l

In fig.2(b), let L be the separation between the two charges.
The potential energy U' = kPQ/L
but L^2 = (2l)^2 + l^2
i.e. L = square-root[5.l^2] = l.[square-root(5)] = 2.236l

Therefore, U' = kPQ/(2.236l) = 0.4472(kPQ/l) = 0.4472 x (2U) = 0.894U
The closest answer is thus option C, which is 0.8U