Question

A disk of radius $\frac{a}{4}$ having a uniformly distributed charge $6$ $C$ is placed in the $x-y$ plane with its centre at $(-\frac{a}{2},0,0)$. A rod of length a carrying uniformly distributed charge $8C$ is placed on the $x-$axis from $x=\frac{a}{4}$ to $x=\frac{5a}{4}$. Two point charges $-7C$ and $3C$ are placed at $(\frac{a}{4},-\frac{a}{4},0)$ and $(-\frac{3a}{4},\frac{3a}{4},0)$ respectively. Consider a cubical surface formed by six surfaces $x=\pm \frac{a}{2},y=\pm \frac{a}{2},z=\pm \frac{a}{2}$. The electric flux through this cubical surface is

• A. $-\frac{2C}{{ϵ}_0}$
• B. $\frac{2C}{{ϵ}_0}$
• C. $\frac{10C}{{ϵ}_0}$
• D. $\frac{12C}{{ϵ}_0}$

Answer 1

The correct option is A $-\frac{2C}{{ϵ}_0}$

From Gauss's Law, we have flux equal to
$\varphi =\frac{\sum Q_{enc}}{{ϵ}_0}=\frac{\left(\frac{8C}{4}\right)-7C+\left(\frac{6C}{2}\right)}{{ϵ}_0}=-\frac{2C}{{ϵ}_0}$
Hence, the correct answer is (A).