Careful measurement of the electric field at the surface of a black box indicate that the net outward flux through the surface of the box is 8.0 \times 10^{3} \mathrm{Nm}^{2} / \mathrm{C} a) What is the net charge inside the box?
Careful measurement of the electric field at the surface of a black box indicate that the net outward flux through the surface of the box is 8.0 \times 10^{3} \mathrm{Nm}^{2} / \mathrm{C} a) What is the net charge inside the box?

Ans: It is given that:
Net outward flux through surface of the box, \phi=8.0 \times 10^{3} \mathrm{Nr}^{2} / \mathrm{C}.
For a body containing net charge a, flux is given by \phi=\frac{q}{\varepsilon_{0}}
where,
\varepsilon_{0}= Permittivity of free space =8.854 \times 10^{-13} \mathrm{~N}^{-1} \mathrm{C}^{2} \mathrm{~m}^{-2}
Therefore, the charge \mathrm{q} is given by \mathrm{q}=\phi \varepsilon_{0}.

    \[\begin{array}{l} \Rightarrow \mathrm{q}=8.854 \times 10^{-12} \times 8.0 \times 10^{3} \\ \Rightarrow \mathrm{q}=7.08 \times 10^{-8} \\ \Rightarrow \mathrm{q}=0.07 \mu \mathrm{C} \end{array}\]