A thin metallic wire having cross-sectional area of is used to make a ring of radius 30 cm. A positive charge of C is uniformly distributed over the ring, while another positive charge of 30 pC is kept at the centre of the ring. The tension in the ring

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Solution

Q.
A thin metallic wire having cross-sectional area of $10^{- 4}$ $m^{2}$ is used to make a ring of radius 30 cm. A positive charge of $2 π$ C is uniformly distributed over the ring, while another positive charge of 30 pC is kept at the centre of the ring. The tension in the ring is ____ N; provided that the ring does not get deformed (neglect the influence of gravity).

(Given, $\frac{1}{4 π ϵ_{0}} = 9 \times 10^{9}$ in SI units) [2024]

Ans.
(3)

$2 T \sin \frac{d θ}{2} = \frac{k q_{0}}{R^{2}} \cdot λ R d θ$ $[λ = \frac{Q}{2 π R}]$

$\Rightarrow T = \frac{k q_{0} Q}{(R^{2}) \times 2 π}$

$= \frac{(9 \times 10^{9}) (2 π \times 30 \times 10^{- 12})}{{(0.30)}^{2} \times 2 π}$

$= \frac{9 \times 10^{- 3} \times 30}{9 \times 10^{- 2}} = 3 N$

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