The electric field at the surface of a black box indicates that the net outward flux through the surface of th

Question

The electric field at the surface of a black box indicates that the net outward flux through the surface of the box is $8.0 	imes 10^3$ Nm$^2$/C. What is the net charge inside the box?

Accepted Answer

According to Gauss's Law, the net electric flux $\Phi_E$ through a closed surface is equal to the net charge $q$ enclosed divided by the permittivity of free space $\varepsilon_0$ ($\Phi_E = q/\varepsilon_0$). 
Given:
$\Phi_E = 8.0 	imes 10^3$ Nm$^2$/C
$\varepsilon_0 \approx 8.854 	imes 10^{-12}$ C$^2$/Nm$^2$

Calculation:
$q = \Phi_E 	imes \varepsilon_0$
$q = (8.0 	imes 10^3) 	imes (8.854 	imes 10^{-12})$
$q = 70.832 	imes 10^{-9}$ C
$q \approx 0.07 	imes 10^{-6}$ C $= 0.07$ μC.
(See NCERT Physics Class 12, Exercise 1.16).

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