Question 617: Electrostatics & Capacitance

Question

Two identical charged spheres are suspended by strings of equal lengths. The strings 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 _______ $$\left(	an 37^{\circ}=\frac{3}{4}ight)$$

Accepted Answer

$$\begin{aligned}
& T \cos 	heta=m g \
& T \sin 	heta=F_e \
& 	an 	heta=\frac{F_e}{m g}
\end{aligned}$$
$$	an 	heta=\frac{F_c}{ho_B V g}$$ ..... (i)
$$	an 	heta=\frac{F_e}{\frac{k}{\left(ho_B-ho_Light) V g}}$$ ..... (ii)
From Eq. (i) & (ii)
$$\begin{aligned}
& ho_{\mathrm{B}} \mathrm{Vg}=\left(ho_{\mathrm{B}}-ho_{\mathrm{L}}ight) \mathrm{kVg} \
& 1.4=0.7 \mathrm{k} \
& \mathrm{k}=2
\end{aligned}$$

Electrostatics & Capacitance

Integer / Numeric Answer Type