Question

Two charged spheres separated at a distance d exert a force F on each other. If they are immersed in a liquid of dielectric constant 2, then the force (if all conditions are same) is:
A) F/2
B) F
C) 2F
D) 4F

Answer 1

The dielectric constant (or relative permeability) of a medium is defined as the ratio of the electrostatic force between two point charges, when placed at the same distance, in a fixed vacuum between the same charges.

Complete step by step solution:
As we know force exerted between two charges in vacuum is
\eqalign{ & \Rightarrow {{F_1 = }}\dfrac{1}{{4\pi {\varepsilon _o}}} \times \dfrac{{{q_1}{q_2}}}{{{r^2}}} \cr & {\text{Force exerted in other medium with dielectric constant k is}} \cr & \Rightarrow {{F_2 = }}\dfrac{1}{k} \times \dfrac{1}{{4\pi {\varepsilon _o}}} \times \dfrac{{{q_1}{q_2}}}{{{r^2}}} \cr & \Rightarrow \dfrac{{F_1}}{{F_2}} = \dfrac{1}{k}{\text{ or,}} \cr & \Rightarrow {{F_2 = }}\dfrac{{F_1}}{k} \cr & \because k = 2,{\text{ given}} \cr & \Rightarrow {\text{force is }}\dfrac{F}{2} \cr} .

Option A is correct.

Note: The dielectric constant does not change because it is a constant. But the relative permeability can vary and the force is inversely proportional. The electrostatic force depends on the magnitude of the charges, the charges between them and the distance between the materials. If everything becomes constant and the dielectric constant increases, the force will mutually decrease.