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 \[8.0 \times {10^3}N{m^2}/C\].
(a) What is the net charge inside the box? (b) 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

Hint: Electric flux represents an electrical field through the number of electrical lines of force of electric field lines that intersect a given area. Electric lines occur on positive electric charges and terminate negative charges. The total outward flux which is passing through any closed surface has a direct proportion relationship to the total electric charge within the closed surface.

Formula used:
To calculate the capacitance of the cylinder we can use
\[C = \dfrac{{2\pi { \in _0}l}}{{{{\log }_e}\dfrac{{{r_1}}}{{{r_2}}}}}\]

Complete step by step solution:
a). Let the total outer flux passing through the surface of the box is \[\phi = 8.0 \times {10^3}N{m^2}/C\]
For the body containing net charge is \[q\]
As we know the flux relation.
\[\phi = \dfrac{q}{{{ \in _0}}}\]
  Where \[{ \in _0} = \]Permittivity of free space
\[{ \in _0} = 8.854 \times {10^{ - 12}}{N^{ - 1}}{C^2}{m^{ - 2}}\]
\[\therefore q = { \in _0}\phi \]
\[ = 8.854 \times {10^{ - 12}} \times 8.0 \times {10^3}\mu C\]
\[ = 7.08 \times {10^{ - 8}}\mu C\]
\[ = 0.07\mu C\]
\[\therefore \] The net charge inside the box is \[0.07\mu C\]
(b) Net piercing out through a body depends on the net charge that the body contains. If the net outward flux through the surface of the box is zero, then the net charge inside the body is zero. The body has an equal amount of positive and negative charges.

Note:
The SI unit of electric flux voltmeters or \[Vm\] which is equivalent to newton-meters square per coulomb or \[N{m^2}{C^{ - 1}}\]. The base units of electrical flux are \[kg.{m^3}.{s^{ - 3}}.{A^{ - 1}}\].
Electric flux calculates the total number of field lines over an area in an electric field. When field lines are entering inside the body, the term is used inward flux to calculate the flux inside the body. And when field lines are coming out of the body, the term is used outward flux to calculate flux outside the body.