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

Options

A. by placing a charge `Q=-q//sqrt(3)` at the centroid of the triangle
B. by placing a charge `Q=q//sqrt(3)` at the centroid of the triangle
C. by placing a charge `Q=q` at the centroid of the triangle
D. by placing a charge `Q=-q` at the centroid of the triangle

Answer

A

Explanation

To keep the systen in equilibrium, net force experiened 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 triangel . Let this charge be '-Q'.

`AD=l cos 30^(@) = (l sqrt(3))/(2), AO=(2)/(3) AD=(1)/(sqrt(3))`
`2|vecF_(CA)|cos 30^(@)=|vecF_(CO)|`
`2xx(1)/(4 pi epsilon_(0))xx(q^2)/(l^2)xx(sqrt(3))/(2)=(1)/(4 pi epsilon_(0))(Qq)/((l//sqrt(3))^(2)) or Q=-(q)/(sqrt(3))`.