Question

Careful measurement of the electric field at the surface of a black
box indicates that the net outward flux through the surface of the
box is $8.0\times {10}^{3}N{m}^2/C.$
What is the net charge inside the box?

If the net outward flux through the surface of the box were zero,
could you conclude that there were no charges inside the box? Why
or Why not?

Answer 1

Here, we have to find the net electric charge inside a box and we have the total outward flux through it, so we have to apply Gauss's theorem.
Using the concept of Gauss's theorem,
Given, Net outward flux $\varphi ==8.0\times {10}^{3}N-m^2/C$
$WeknowthatNetflux\varphi =\frac{Charge}{{\epsilon }_0}=\frac{q}{{\epsilon }_0}\Rightarrow q={\epsilon }_0\varphi FromGaus{s}^{\prime }stheoremq==0.07\times {10}^{-6}C=0.07\mu C$
The flux is outward hence the charge is positive in nature.

Here, we have to find the net electric charge inside a box and we have the total outward flux through it, so we have to apply Gauss's theorem.
But Net outward flux=0.
Then, we can conclude that the net charge inside the box is zero, i.e., the box may have either zero charge or have equal amount of positive and negative charges. It means we cannot conclude that there is no charge inside the box.