Solveeit Logo

Question

Question: The electric flux through a closed surface is found to be 780N−m²/C Approximately what quantity of c...

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?

Explanation

Solution

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 ϕtotal=780Nm2/C{\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,
ϕtotal=qen0{\phi _{total}} = \dfrac{{{q_{en}}}}{{{ \in _0}}}
Or,qen=ϕtotal0{q_{en}} = {\phi _{total}}{ \in _0}
Now put the value on the above equation ϕtotal=780Nm2/C{\phi _{total}} = 780N - {m^2}/C
Or,qen=(780Nm2)(8.87×1012){q_{en}} = (780N - {m^2})(8.87 \times {10^{ - 12}})...........[the value of 0{ \in _0} is 8.8710128.87*10^{-12}]
qen=6.90×109C=6.90nC\Rightarrow {q_{en}} = 6.90 \times {10^{ - 9}}C = 6.90nC
So, the total quantity of charge is 6.90nC6.90nC.

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.