Three charges Q, `+q` and `+q` are placed at the vertices of a right-angled isosceles triangle as shown. The net electrostatic energy of the configuration is zero if Q is equal to

Options

A. `(-q)/(1 + sqrt(2))`
B. `(-2q)/(2 + sqrt(2))`
C. `-2q`
D. `+q`

Answer

B

Explanation

`U = (1)/(4 pi in_(0)) [ (Qq)/(a) + (q.q)/(a) + (Qq)/(sqrt(2) a)] = 0`
`Q + q + (Q)/(sqrt(2)) = 0`
`((sqrt(2) + 1)Q)/(sqrt(2)) = -q`
`Q = (-sqrt(2) q)/((sqrt(2) + 1)) = (2q)/((2 + sqrt(2)))`