Question

Two identical charged spheres are suspended strings of equal lengths. The strings make an angle of ${30}^0$ with each other. When suspended in a liquid of density of $0.8gc{m}^{-3}$, the angle remains the same! if te density of the material of the sphere is $1gc{m}^{-3}$ , the dielectric cons ant of the liquid is

Answer 1

$\tan \theta =\frac{F}{\rho vg}=\frac{\left(F/\epsilon r\right)}{\left(\rho -\sigma \right)vg}$

$\Rightarrow \frac{\rho }{\rho -\sigma }=\epsilon r$

$\Rightarrow \frac{1}{1-0.8}=\epsilon r$

$\Rightarrow 5=\epsilon r$

$\Rightarrow \epsilon r=5$

$\therefore$ dielectric current $=5$