Electrostatics 3 Question 9
9. A disc of radius $\frac{a}{4}$ having a uniformly distributed charge $6 \mathrm{C}$ is placed in the $x-y$ plane with its centre at $\frac{-a}{2}, 0,0$. 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 $-7 \mathrm{C}$ and $3 \mathrm{C}$ are placed at $\frac{a}{4}, \frac{-a}{4}, 0$ and $\frac{-3 a}{4}, \frac{3 a}{4}, 0$, 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
(2009)
(a) $\frac{-2 \mathrm{C}}{\varepsilon_{0}}$
(b) $\frac{2 \mathrm{C}}{\varepsilon_{0}}$
(c) $\frac{10 \mathrm{C}}{\varepsilon_{0}}$
(d) $\frac{12 \mathrm{C}}{\varepsilon_{0}}$
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Answer:
Correct Answer: 9. (a)
Solution:
- Total enclosed charge as already shown is
$ q_{\mathrm{net}}=\frac{6 C}{2}+\frac{8 C}{4}-7 C=-2 C $
From Gauss-theorem, net flux, $\varphi_{\text {net }}=\frac{q_{\text {net }}}{\varepsilon_{0}}=\frac{-2 C}{\varepsilon_{0}}$
