Initially, the forces acting on each sphere are as follows:

(i) Weight,

(ii) Tension in the string, T

(iii) Electrostatic force of repulsion, F

For equilibrium of sphere

and (ii)

Divide (i) by (ii), we get

When they are suspended in a liquid of density σ and dielectric constant K, the angle θ and hence the distance between the spheres remains the same. Therefore,

Force of repulsion will become

and weight will become

….(v)

Let T v is the new tension in string. For equilibrium of sphere,

Divide (vi) by (vii), we get

(Using (iv) and (v))

From equations (iii) and (viii), we get