Question

Two spheres of equal mass are suspended by light-weight strings of length 15 cm each. When a charge of -4 nC is put on each sphere, each string makes an angle of 30° with the vertical in equilibrium. What is the mass of the sphere?

Answer 1

Force on shpere by Electric(E) and Magnetic(B) field is given by Lorentz
F = q x ( E + v x B)

When the sphere is moving, magnetic force(qxvxB), But the given condition the spheres in equilibium(I think they do not moving), so the net force is F = qxE

and we also consider the mechanical force of the spheres by the gravitational force given by the gravitational field and string tension(T)

Consequently the force of sphere in equilbrium is

F = q(E + vxB) + mG + T = qE + mG + T = 0

there is also the equation of rotational equilibrium, called Moment(or Torque), used by the nonrotating object or constant speed rotationg object

M = r x F = 0

if you use these equation, i think you will find the answer

but, care should be given that the frame of this problem is gravitatinally no rotating and no moving(because it contains relativistic effects)