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A disk of radius $a / 4$ having a uniformly distributed charge $6 C$ is placed in the $x-y$ plane with its centre at $(-a / 2,0,0)$. A rod of length $a$ carrying a uniformly distributed charge $8 C$ is placed on the $x$-axis from $x=a / 4$ to $x=5 a / 4$. Two point charges $-7 C$ and $3 C$ are placed at $(a / 4,-$ $a / 4,0)$ and $(-3 a / 4,3 a / 4,0)$, respectively. Consider a cubical surface formed by six surfaces $x=\pm a / 2, y=\pm a / 2, z=\pm a / 2$. The electric flux through this cubical surface is
$\frac{-2\,C }{\varepsilon_0}$
$\frac{2\,C }{\varepsilon_0}$
$\frac{10\,C }{\varepsilon_0}$
$\frac{12\,C }{\varepsilon_0}$
Solution
Flux $=\frac{\text { Total charge }}{\varepsilon_0}$
Total charge $=$ half of charge of disk $+\frac{1}{4}$ th of charge of rod $+(-7 C)$
$=3+\frac{1}{4} \times 8-7$
$=3+2-7$
$=-2 C$
Flux $=\frac{-2 C}{\varepsilon_0}$
