Three positive charges of equal magnitude q are placed at the vertices of equilateral triangle of side l. How can the system of charges be placed in equilibrium?

Options

A. `Q=q/(sqrt(12))`
B. `Q=q/(sqrt(2))`
C. `Q=q/(sqrt(3))`
D. `Q=-q/(sqrt(3))`

Answer

C

Explanation

To keep the system in equilibrium, the net force experienced by charges at A, B and C should be zero. For this another charge of opposite sign should be placed at the centroid of the triangle. Let this charge be -Q.

`AD=l cos 30^(@)=(l sqrt(3))/2`
`AO=2/3 AD = (l)/(sqrt(3))=CO`
`2|vec F_(CA)| cos30^(@)=|vec F_(CO)|`
`|vec F_(CB)|=|vec F_(CA)|`
`2(1)/(4 pi epsilon) (q^(2))/(l^(2)) (sqrt(3))/(2)=(1)/(4 pi epsilon) (Qq)/(l//sqrt(3))` or `Q=q/(sqrt(3))`.