Question

The electric flux through a closed surface is found to be 780N−m²/C Approximately what quantity of charge is enclosed by the surface in nC?

Answer 1

Hint
 We use gauss’s law to find the total quantity of charge is enclosed by the surface.
According the question we get,
Total flux ${\phi _{total}} = 780N - {m^2}/C$
Now the electric flux is a property of an electric field that may be thought of as the number of electric lines of force (or electric field lines) that intersect a given area.

Complete step by step answer
By the gauss’s law the flux through closed surface is,
${\phi _{total}} = \dfrac{{{q_{en}}}}{{{ \in _0}}}$
Or,${q_{en}} = {\phi _{total}}{ \in _0}$
Now put the value on the above equation ${\phi _{total}} = 780N - {m^2}/C$
Or,${q_{en}} = (780N - {m^2})(8.87 \times {10^{ - 12}})$...........[the value of ${ \in _0}$ is $8.87*10^{-12}$]
$ \Rightarrow {q_{en}} = 6.90 \times {10^{ - 9}}C = 6.90nC$
So, the total quantity of charge is $6.90nC$.

Note
In physics, Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field. The surface under consideration may be a closed one enclosing a volume such as a spherical surface.We choose a Gaussian surface, such that evaluation of the electric field becomes easy. Make use of symmetry to make problems easier.