Electrostatics Question 15
Question 15 - 2024 (30 Jan Shift 2)
Two identical charged spheres are suspended by string of equal lengths. The string make an angle of $37^{\circ}$ with each other. When suspended in a liquid of density $0.7 \mathrm{~g} / \mathrm{cm}^{3}$, the angle remains same. If density of material of the sphere is $1.4 \mathrm{~g} / \mathrm{cm}^{3}$, the dielectric constant of the liquid is $\left(\tan 37^{\circ}=\frac{3}{4}\right)$.
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Answer: (2)
$\mathrm{T} \cos \theta=\mathrm{mg}$
$\mathrm{T} \sin \theta=\mathrm{F}_{\mathrm{e}}$
$\tan \theta=\frac{\mathrm{F}_{\mathrm{e}}}{\mathrm{mg}}$
$\tan \theta=\frac{F_{e}}{\rho_{\mathrm{B}} V g}$
$\tan \theta=\frac{F_{e}}{\frac{k}{\left(\rho_{B}-\rho_{L}\right) V g}}$.
From Eq. (i) $\backslash &$ (ii)
$\rho_{\mathrm{B}} \mathrm{Vg}=\left(\rho_{\mathrm{B}}-\rho_{\mathrm{L}}\right) \mathrm{kVg}$
$1.4=0.7 \mathrm{k}$
$\mathrm{k}=2$
