Question

A charge Q is distributed uniformly on a ring of radius r a sphere of equal radius is constructed with its centre at Periphery Of Rings find electric flux through surface of a sphere

Answer 1

Dear Student,
$$\begin{gathered} LetcenterofringbeOandSpherecenterbeO\text{'} \\ LetP,Qareintersectionpoints \\ OO\text{'}bisectsPQintwoequalparts, \\ Sisthebisectingpoint \\ POS,QOSformsarightangletriangle \\ PO=r,OS=r/2 \\ \angle POS=\theta \\ \cos \theta =\frac{OS}{PS}=0.5 \\ \theta ={60}^{\circ } \\ anglesubtendendedbyringis2\theta ={120}^{\circ } \\ For2\mathrm{\pi }\mathrm{radians},\mathrm{charge}\mathrm{is}\mathrm{q} \\ \mathrm{for}2\mathrm{\pi }/3\mathrm{radians},\mathrm{charge}\mathrm{is}\mathrm{q}/3 \\ \mathrm{\varphi }=\frac{\mathrm{q}}{3{\mathrm{\epsilon }}_0} \end{gathered}$$