Question

Two charges of magnitudes -2Q and +Q are located at points (a,0) and (4a, 0) respectively. What is the electric flux due to these charges through a sphere of radius '3a' with its center at the origin?

Answer 1

Using Gauss's law

$Flux\left(\varphi \right)=\frac{q}{{ϵ}_0}$

where, q is the total charge inside the surface

Here, $q=-2Q$ and gaussian surface is a sphere of radius 3a and center at origin.

So,$Flux\left(\varphi \right)=\frac{-2Q}{{ϵ}_0}$

Here, flux is only due to charge -2Q because no. of field lines enter the sphere due to charge +Q is equal to no. of field lines coming out of the sphere, so net flux is zero due to charge +Q.