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Question

A point charge $$Q$$ is located on the axis of a disc of radius $$R$$ at a distance $$a$$ from the plane of the disc. If one fourth (1/4th) of the flux from the charge passes through the disc, the relation between $$a$$ and $$R$$ is $$a=\frac { R }{ \sqrt { x }  } $$.Find $$x$$.
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Solution

solid angle subtended by ring is $$2\pi(1-cos\theta)$$...(i)
given the flux through the disc is 1/4th of total flux, the solid angle subtended by disc will be 1/4th of total solid angle which is $$\dfrac { 1 }{ 4 } 4\pi=\pi $$from equation (i)
$$2\pi(1-cos\theta)=\pi \Rightarrow cos\theta=\dfrac { 1 }{ 2 }$$ from geometry $$cos\theta=\dfrac { a }{ \sqrt { a^2+R^2 } }=\dfrac{ 1 }{ 2 }$$
$$ \Rightarrow a=\dfrac { R }{ \sqrt { 3 } }$$
hence correct answer is 3.

Physics

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