Question

Flux passing through shaded surface of sphere when a point charge $q$ is placed at the centre is (radius of the sphere is $R$ )

• A. $q/{\epsilon }_0$
• B. $q/2{\epsilon }_0$
• C. $q/4{\epsilon }_0$
• D. zero

Answer 1

Answer: (C)

$\alpha =60^{\circ }$
Solid angle subtended by $BCD$, $\Omega =2\pi (1-\cos \alpha )=\pi$
Solid angle subtended by $ABDE$,
${\Omega }_{(ABCDE)}-{\Omega }_{(BCD)}=2\pi -\pi =\pi$
Hence, flux through $ABDE:\varphi =\frac{q}{{\epsilon }_0}\frac{\pi }{4\pi }=\frac{q}{4{\epsilon }_0}$