Q 12-01-042JEE MainJEE Main 2024 (1 Feb, Shift 1)Medium
Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle $\theta$ with each other. When suspended in water the angle remains the same. If the density of the material of the spheres is $1.5\ \text{g/cc}$, the dielectric constant of water will be ______. (Take density of water $= 1\ \text{g/cc}$)
Numerical value type. Enter your answer.
Answer: 3
In air: $\tan\dfrac{\theta}{2} = \dfrac{F}{mg}$.
In water the electric force becomes $F/K$ and the effective weight becomes $mg\left(1 - \dfrac{\sigma}{\rho}\right)$. Since the angle is unchanged,
$$\frac{F}{mg} = \frac{F/K}{mg(1 - \sigma/\rho)} \Rightarrow K = \frac{\rho}{\rho - \sigma} = \frac{1.5}{1.5 - 1} = 3$$
Solution by Sreeraj P, M.Sc Physics