Question

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

Answer 1

Please find the attached graphical representation of the solution.

Answer 2

Assume that the sphere is in the Gaussian surface.

Now refer to the Attachment.

Electric flux is due to the charge enclosed through the Gaussian surface, not by the charge which is outside from this surface.

Now Flux due to -2q.

= E. (4πR²)

= -2q $\frac{-2q}{4\pi\epsilon_0 r} * 4\pi R^2$

= $-\frac{2q }{\epsilon_0 2a} * (3a)^2$

= $-\frac{q}{\epsilon_0} * 9a$

Now flux due to + q

= E. (4πR²)

$\frac{q}{4\pi\epsilon_0 (4a-3a)} * 4\pi (3a)^2$

$\frac{q}{\epsilon_0} * 9a$

Total Flux = $\frac{q}{\epsilon_0} * 9a$ $-\frac{q}{\epsilon_0} * 9a$

= 0

Hope it Helps :-)