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Two identical balls each having a density $ρ$ are suspended from a common point by two insulating strings of equal length. Both the balls have equal mass and charge. In equilibrium each string makes an angle $θ$ with the vertical. Now both the balls are immersed in a liquid. As a resultant the angle $θ$ does not change. The density of liquid is $σ$ . Find the dielectric constant of the liquid.

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$\frac{ρ}{ρ - σ}$

$\frac{σ}{ρ - ρ}$

$\frac{ρ - σ}{ρ}$

$\frac{p - σ}{σ}$

answer is A.

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Detailed Solution

In equlibrium, F_e = mg tan $θ$

In air, $\frac{1}{4 {πε}_{0}} \frac{q^{2}}{r^{2}} = mgtan θ$ . . . . (1)

In liquid, $\frac{1}{4 {πkε}_{0}} \frac{q^{2}}{r^{2}} = mg [1 - \frac{σ}{ρ}] \tan θ$ . . . . . (2)

$\frac{(1)}{(2)} \Rightarrow k = \frac{ρ}{ρ - σ}$

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