Question 723: Electrostats & Capacitance

Question

A thin metallic wire having cross sectional area of $$10^{-4} \mathrm{~m}^2$$ is used to make a ring of radius $$30 \mathrm{~cm}$$. A positive charge of $$2 \pi \mathrm{~C}$$ is uniformly distributed over the ring, while another positive charge of 30 $$\mathrm{pC}$$ is kept at the centre of the ring. The tension in the ring is ______ $$\mathrm{N}$$; provided that the ring does not get deformed (neglect the influence of gravity). (given, $$\frac{1}{4 \pi \epsilon_0}=9 	imes 10^9$$ SI units)

Accepted Answer

$$\begin{aligned}
& 2 \mathrm{~T} \sin \frac{\mathrm{d} 	heta}{2}=\frac{\mathrm{kq}_0}{\mathrm{R}^2} \cdot \lambda \mathrm{Rd} 	heta \\
& {\left[\lambda=\frac{\mathrm{Q}}{2 \pi \mathrm{R}}ight]}
\end{aligned}$$
$$\begin{aligned}
& \Rightarrow \mathrm{T}=\frac{\mathrm{Kq}_0 \mathrm{Q}}{\left(\mathrm{R}^2ight) 	imes 2 \pi} \\
& =\frac{\left(9 	imes 10^9ight)\left(2 \pi 	imes 30 	imes 10^{-12}ight)}{(0.30)^2 	imes 2 \pi} \\
& =\frac{9 	imes 10^{-3} 	imes 30}{9 	imes 10^{-2}}=3 \mathrm{~N}
\end{aligned}$$

Electrostats & Capacitance

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