Question

A point charge causes an electric flux of $–1.0\times {10}^{3}N{m}^2/C$ to pass through a spherical Gaussian surface of 10.0 cm radius centred on the charge.
If the radius of the Gaussian surface were doubled, how much flux would pass through the surface?

What is the value of the point charge?

Answer 1

As we know the electric flux passing through any surface is independent of the radius of Guassian surface, so if the radius of Guassian surface were doubled, the electric flux linked with the surface remains same $(\varphi =\frac{q}{{\epsilon }_0})$. It depends only on charge.

$\varphi =-1.0\times {10}^{3}N-m^2/C$
Radius=10.0cm
Using Guass's theorem,
The flux linked $\varphi =\frac{q}{{\epsilon }_0}q=\varphi {\epsilon }_0=-1.0\times {10}^3\times 8.854\times {10}^{-12}=-8.85\times {10}^{-9}C$
Thus, the value of point charge is $-8.85\times {10}^{-9}C$