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AIIMS 2008
Exam
AIIMS
Year
2008
Subject
Physics
Chapter
Electrostatics

AIIMS 2008 · Physics · Electrostatics

A charge q is uniformly distributed on a ring of radius r . A...

A charge qq is uniformly distributed on a ring of radius rr. A sphere of an equal radius is constructed with its centre lying on the periphery of the ring. The flux of electric field through the surface of the sphere will beA charge q is uniformly distributed on a ring of radius r . A sphere of an equal radius is constructed with its centre

Options

  1. A(\frac{q}{\varepsilon_0})
  2. B(\frac{q}{2 \varepsilon_0})
  3. C(\frac{q}{3 \varepsilon_0})
  4. D(\frac{q}{4 \varepsilon_0})

Correct answer

C. (\frac{q}{3 \varepsilon_0})

Step-by-step solution

A charge q is uniformly distributed on a ring of radius r . A sphere of an equal radius is constructed with its centre
Charge on ring qq, centre of ring =O=O Centre of sphere =O′=O^{\prime} Linear charge density of ring, λ=q2πa\lambda=\frac{q}{2 \pi a} Charge on arc ABA B of ring, qAB=λ(arc⁡AB)=12πa⋅q⋅2πa3qAB=q/3\begin{aligned} & q_{A B}=\lambda(\operatorname{arc} A B)=\frac{1}{2 \pi a} \cdot q \cdot \frac{2 \pi a}{3} \\ & q_{A B}=q / 3\end{aligned} i.e., charge enclosed by sphere =q/3∴=q / 3 \therefore Flux coming out of sphere =q/3ε0=q / 3 \varepsilon_0.
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