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 $\left(\frac{-a}{2}, 0,0\right)$. A rod of length a carrying a uniformly distributed charge $8\, C$ is placed on the x-axis from $x=\frac{a}{4}$ to $x=\frac{5 a}{4}$. Two point charges - $7\, C$ and $3\, C$ are placed at $\left(\frac{a}{4}, \frac{-a}{4}, 0\right)$ and $\left(\frac{-3 a}{4}, \frac{3 a}{4}, 0\right)$, 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. $\frac{-2C}{\varepsilon_0}$
• B. $\frac{2C}{\varepsilon_0}$
• C. $\frac{10C}{\varepsilon_0}$
• D. $\frac{12C}{\varepsilon_0}$

Answer 1

Answer: (A)

Total enclosed charge as already shown is
$q_{net}=\frac{6C}{2}+\frac{8C}{4}-7C=-2C$
From Gauss-theorem, net flux,
$\phi_{net}=\frac{q_{net}}{\varepsilon_0}+\frac{-2C}{\varepsilon_0}$