Question

The flux of electric field due to the these charges through the surface $S$ is:

• A. $\frac{-q}{{\epsilon }_0}$
• B. $\frac{q}{{\epsilon }_0}$
• C. $\frac{3q}{{\epsilon }_0}$
• D. $\frac{5q}{{\epsilon }_0}$

Answer 1

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

As from the figure we can conclude that the charged enclosed by gaussion surface is $2q-3q$, hence, using the gauss law,

i.e. $\varphi =\frac{Q_{inc}}{{\epsilon }_0}$

where $Q_{inc}=+2q-3q=-q$

$\therefore \varphi =\frac{-q}{{\epsilon }_0}$

Note : Here $+2q$ charge is outside the sphere and thus does not be included in the net charge enclosed by the sphere.

$\therefore$ Option (A) is the correct answer.