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Q.

A charge Q is distributed uniformly on a ring of radius r. A sphere of equal radius r is constructed with its centre at the periphery of the ring. The flux of the electric field through the surface of the sphere is $\frac{Q}{{nε}_{0}}$ . The value of n is :

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Detailed Solution

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on considering the triangle $∆ OO' A$

$\frac{θ}{2} = 60 °$

$θ = 120 °$

$ℓ = Rθ = R (\frac{2 π}{3})$

$q_{in} = (\frac{q}{2 πR}) (R (\frac{2 π}{3})) = \frac{q}{3}$

flux through the sphere is given by $ϕ$

$ϕ = \frac{q_{in}}{ϵ_{0}} = \frac{q}{3 ϵ_{0}}$

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A charge Q is distributed uniformly on a ring of radius r. A sphere of equal radius r is constructed with its centre at the periphery of the ring. The flux of the electric field through the surface of the sphere is Qnε0. The value of n is :