Electrostatics 3 Question 15
15. A cubical region of side $a$ has its centre at the origin. It encloses three fixed point charges, $-q$ at $(0,-a / 4,0),+3 q$ at $(0,0,0)$ and $-q$ at $(0,+a / 4,0)$. Choose the correct option(s).
(2012)
(a) The net electric flux crossing the plane $x=+a / 2$ is equal to the net electric flux crossing the plane $x=-a / 2$
(b) The net electric flux crossing the plane $y=+a / 2$ is more than the net electric flux crossing the plane $y=-a / 2$
(c) The net electric flux crossing the entire region is $q / \varepsilon_{0}$
(d) The net electric flux crossing the plane $z=+a / 2$ is equal to the net electric flux crossing the plane $x=+a / 2$
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Answer:
Correct Answer: 15. (a,c)
Solution:
- Option (a) is correct due to symmetry.
Option (b) is wrong again due to symmetry.
Option (c) is correct because as per Gauss’s theorem, net electric flux passing through any closed surface $=\frac{q_{\text {in }}}{\varepsilon_{0}}$
Here, $\quad q_{\text {in }}=3 q-q-q=q$
$\therefore \quad$ Net electric flux $=\frac{q}{\varepsilon_{0}}$
Option (d) is wrong because there is no symmetry in two given planes.
