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+(3kQ.q)/(a//sqrt(3))` where q is the charge brought at the centre , `U_(f)=0 rArr q=(-Q)/(sqrt(3))`