Question

In $\text{XY}-$plane, there is surface charge density of $5\times {10}^{-16}{\text{Cm}}^{-2}$ on a long uniformly charged sheet. A circular loop of radius $0.1\text{m}$ makes an angle of ${60}^{\circ }$ with $\text{Z-}$axis. Determine the electric flux through the loop ?

• A. $7.68\times {10}^{-9}{\text{Nm}}^2{\text{C}}^{-1}$
• B. $7.68\times {10}^{-7}{\text{Nm}}^2{\text{C}}^{-1}$
• C. $9.46\times {10}^{-7}{\text{Nm}}^2{\text{C}}^{-1}$
• D. $9.46\times {10}^{-9}{\text{Nm}}^2{\text{C}}^{-1}$

Answer 1

The correct option is B $7.68\times {10}^{-7}{\text{Nm}}^2{\text{C}}^{-1}$

Given,
surface charge density,$\sigma =5.0\times {10}^{-16}{\text{Cm}}^{-2}$
radius of circular loop, $r=0.1\text{m}$
$\theta ={60}^{\circ }$

We know that electric field due to uniformly charged sheet,
$E=\frac{\sigma }{2{\epsilon }_0}$

Flux $\left(\varphi \right)$ passing through circular surface will be
$\varphi =\oint EdS\sin \theta$

Substituting the values of surface area of circular loop $dS$, $\theta$ and $E$ we get
$\varphi =\frac{\sigma }{2{ϵ}_0}\times \pi r^2\sin \theta$

$\Rightarrow \varphi =\frac{5.0\times {10}^{-16}\times 3.14\times (0.1{)}^2\sin {60}^{\circ }}{2\times 8.85\times {10}^{-12}}$

$\Rightarrow \varphi =7.68\times {10}^{-7}{\text{Nm}}^2{\text{C}}^{-1}$

Hence option (a) is the correct answer.