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 $(\frac{-a}{2},0,0).A$rod of length a carrying a uniformly distributed charge 8 C is placed on the x-axis from $x=\frac{a}{4}tox=\frac{5a}{4}.$Two point charges –7 C and 3 C are placed at $(\frac{a}{4},\frac{-a}{4},0)and(\frac{-3a}{4},\frac{3a}{4},0),$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:

• A. $\frac{-2C}{{\epsilon }_0}$
• B. $\frac{2C}{{\epsilon }_0}$
• C. $\frac{10C}{{\epsilon }_0}$
• D. $\frac{12C}{{\epsilon }_0}$

Answer 1

The correct option is A $\frac{-2C}{{\epsilon }_0}$

The point charge of 3C lies outside the Gaussian surface. Therefore, charge enclosed by Gaussian surface,
$q=q_{disk}+q_{rod}+q_{point}=\frac{6C}{2}+\frac{8C}{4}+(-7C)=-2CElectricflux=\frac{q}{{\epsilon }_0}=\frac{-2C}{{\epsilon }_0}$