Question

Consider a circle of radius $R$. A point charge lies at a distance $a$ from its center and on its axis such that $R=a\sqrt{3}$. If electric flux passing through the circle is $\varphi$, find the magnitude of the point charge.

Answer 1

Given radius $=R$

also, $R=a\sqrt{3}$,

So, flux through a sphere of radius $R$ is given by, ${\varphi }^1=\frac{Q_{inc}}{{\epsilon }_0}$

$\Rightarrow$ By on area of ${4\pi R}^2$, ${\varphi }^1=\frac{Q}{{\epsilon }_0}$

But by or area of ${\pi r}^2$, $\varphi =\frac{Q}{{4\epsilon }_0}$

$\Rightarrow$ flux through the area of circle given by $\varphi =\frac{Q_{inc}}{{4\epsilon }_0}$

$\Rightarrow Q_{inc}=\varphi {4\epsilon }_0$

$\Rightarrow$ Option (D) is the correct answer.