Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 45° with each other. When the system is immersed in a liquid of relative density 0.8, the angle between the strings remains unchanged. If the density of the material of the sphere is 2.4 gcm ⁻³ , what is the dielectric constant of the liquid?

Step-by-step solution

Let the tension in the string be T and the angle made by each string with the vertical be . In air, the forces acting on each sphere are the electrostatic force F , the weight mg , and the tension T . For equilibrium, T = F T = mg Dividing the two equations, we get = F mg . When immersed in the liquid, the electrostatic force becomes F' = F K , where K is the dielectric constant of the liquid. The effective weight of the sphere becomes W' = mg - F_b = mg - V _l g = mg (1 - _l _s ) , where _l is the density of the l