Question

Two charged spheres of charge q and mass m are each hanging from strings and are at equilibrium as shown below:

Give an expression for tanθ in terms of ke (use "k" to write ke), q, m, g (gravity), and d (the distance between the spheres).

tanθ=

Answer 1

call angle from vertical A and tension in string = T
m g =

horizontal components
F = k q^2/d^2 = T sin A
vertical components
m g = T cos A
then
T sin A/T cos A= tan A = k q^2/(m g d^2)