Three charges, each of value Q, are placed at the vertices of an equilateral triangle. A fourth charge q is placed at the centre of the triangle. If the charges remains stationary then, q = …………………

Options

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

Answer

B

Explanation

`OA=(2)/(3)(asin60^(@))=(a)/(sqrt(3)), F_(1)=2Fcos30^(@)=(2kQ^(2))/(a^(2)).sqrt(3)/(2)=(sqrt(3)kQ^(2))/(a^(2))`,
Force on charge Q at A due to q,
`F_(2)=(3kQq)/(a^(2))`
`F_(1)=F_(2)`,
`(sqrt(3)kQ^(2))/(a^(2))=-(3kQq)/(a^(2)),q=(-Q)/(sqrt(3))`