Two metal spheres of identical mass m 340g are suspended by

Two metal spheres of identical mass m = 3.40g are suspended by light strings 0.500m in length. The left-hand sphere carries a charge of 0.885 µC,and the right-hand sphere carries a charge of 1.57 µC. What is the equilibrium separation between the centers of the two spheres? (In metres)

Solution

Resolving forces

We have in horizontal direction T cos (theta) = F (electric)

T sin(theta) = F(gravity)

So Tan(theta) = 3.4 * 10^-3 * 9.8 / (9* 10^9 * 1.57* 10^-6 * 0.885 * 10^-6 /r^2)

sqrt( 0.5^2 - (r^2/4) ) / ( r/2) = 3.4 * 10^-3 * 9.8 / (9* 10^9 * 1.57* 10^-6 * 0.885 * 10^-6 /r^2)

r = 0.656 m