A thin metallic wire having cross sectional area of 10–4m2 is used to make a ring of radius 30 cm. A positive charge of 2πC 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).

Engineering

Physics

Charge and Coulombs Law

Equilibrium of Forces

Question

A thin metallic wire having cross sectional area of 10^–4m² is used to make a ring of radius 30 cm. A positive charge of 2πC 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). $(given, \frac{1}{4 ϵ_{0}} = 9 \times 10^{9} units)$

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$2 Tsin \frac{dθ}{2} = \frac{kQq}{R^{2}} (\frac{dθ}{2 π})$

$\Rightarrow T = \frac{kQq}{2 {πR}^{2}}$

$\Rightarrow T = \frac{9 \times 10^{9} \times 30 \times 10^{- 12} \times 2 π}{2 π (0.3)^{2}}$

⇒ T = 3 N