Two charged spheres separated by a distance 'd' exert some force on each other. If they are immersed in a liquid of dielectric constant 2, then what is the force exerted, if all other conditions are same?

F/2

F

2F

4F

Solution

F/2

Given:-

Distance between two charges = d

and dielectric constant (k) = 2

Force between charged spheres

(F) = $\frac{1}{4 π ε_{0}} \times \frac{q_{1} q_{2}}{r_{2}}$

where ε₀ is permitivity of free space.

Force for a medium with dielectric constant k

F' = $\frac{1}{k} \times \frac{1}{4 π ε_{0}} \times \frac{q_{1} q_{2}}{r^{2}}$

= $\frac{F}{k}$

F' = $\frac{F}{2}$

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