Question

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 30° with each other. When suspended in a liquid of density 0.8gcm^–3, the angle remains the same. If density of the material of the sphere is 1.6gcm^–3, the dielectric constant of the liquid is

(a) 1 

(b) 4 

(c) 3 

(d) 2

Answer 1

Initially, the forces acting on each ball are
(i) Tension T
(ii) Weight mg
(iii) Electrostatic force of repulsion F
For its equilibrium along vertical,
Tcosθ = mg ...(i)
and along horizontal,
Tsinθ = F ...(ii)
Dividing equation (ii) by (i), we get

tanθ = F/mg   ...(iii)

When the balls are suspended in a liquid of density σ and dielectric constant K, the electrostatic force will become (1/K) times, i.e. F′ = (F/K) while weight