Q.
A disk of radius $a/4$ having a uniformly distributed charge $6C$ 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 $8C$ is placed on the $x$-axis from $x = a/4$ to $x = 5a/4$. Two point charges $- 7C$ and $3C$ are placed at $(a/4, - a/4,0)$ and $( - 3a/4,3a/4,0),$ 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
A) $\frac{- 2C}{\varepsilon_{0}}$
B) $\frac{2C}{\varepsilon_{0}}$
C) $\frac{10C}{\varepsilon_{0}}$
D) $\frac{12C}{\varepsilon_{0}}$
Explanation
(a) Half disk (charge $3C$), and fourth part of rod (charge $2C$) and charge of $- 7C$ are inside the cubical surface, so net charge inside the surface $= 3 + 2 - 7 = - 2C$
$\therefore$ Flux through the surface $\phi = \frac{1}{\varepsilon_{0}}(Q) = \ \frac{- 2C}{\varepsilon_{0}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.