Question

A point charge $+10\text{nC}$ is located on the axis of a disc of radius $1\text{m}$ at a distance of $\sqrt{3}\text{m}$ from the plane of the disc as shown in the figure. The electric flux from the charge passing through the disc is
(Take ${ϵ}_o=9\times {10}^{-12}{\text{C}}^2/{\text{N-m}}^2$)

• A. $64.4{\text{N-m}}^2/\text{C}$
• B. $74.4{\text{N-m}}^2/\text{C}$
• C. $84.4{\text{N-m}}^2/\text{C}$
• D. $94.4{\text{N-m}}^2/\text{C}$

Answer 1

The correct option is B $74.4{\text{N-m}}^2/\text{C}$


The given disc can be assumed to be the base of an imaginary cone having semi-vertex angle $\theta$.

From geometry, $\tan \theta =\frac{1}{\sqrt{3}}$

$\Rightarrow \theta ={30}^{\circ }$

Now, by Gauss's law, electric flux through a cone is,

$\varphi =\frac{q}{2{ϵ}_0}(1-\cos {30}^{\circ })$

$\varphi =\frac{10\times {10}^{-9}}{2\times 9\times {10}^{-12}}(1-\cos {30}^{\circ })$

$\varphi =74.4{\text{N-m}}^2/\text{C}$