Three equal charges `Q` are placed at the three vertices of an equilateral triangle. What should be the va,ue of a charge, that when placed at the centroid, reduces the interaction energy of the system to zero ?

Options

A. `(-Q)/(2)`
B. `(-Q)/(3)`
C. `(-Q)/(2sqrt(3))`
D. `(-Q)/(sqrt(3))`

Answer

D

Explanation

`U_(1) = (3KQ^(2))/(a)` where `a =` side of equilateral triangle
`U_(1) = (3kQ^(2))/(a) + (3kQq)/(a//sqrt(3))` where `q` is the charge brought
at the centre , `U_(f) = 0 rArr q = (-Q)/(sqrt(3))`.