Question

The net outward flux through surface of a box is \( 8.0\times10^{3}~\text{Nm}^{2}\text{C}^{-1} \). The net charge inside the box is (approximately):

• A. 70 nC
• B. 42 nC
• C. 21 nC
• D. 60 nC

Hint:

Gauss's law states that the net outward flux depends strictly on the total charge enclosed inside the boundary shape, completely independent of how those charges are distributed or the specific geometric dimensions of the enclosing container.

Answer 1

The Correct Option is A

Step 1: Recall Gauss's law.
Gauss's law says the total electric flux coming out of a closed surface depends only on the charge sitting inside it: \[ \phi = \frac{q_{in}}{\varepsilon_0} \]
Step 2: Rearrange to find the charge.
We want the enclosed charge, so multiply both sides by $\varepsilon_0$: \[ q_{in} = \phi\,\varepsilon_0 \]
Step 3: Note the constant.
The permittivity of free space is $\varepsilon_0 = 8.854\times10^{-12}\ \text{C}^{2}\text{N}^{-1}\text{m}^{-2}$.
Step 4: Put in the given flux.
The flux is $\phi = 8.0\times10^{3}\ \text{Nm}^{2}\text{C}^{-1}$: \[ q_{in} = (8.0\times10^{3})(8.854\times10^{-12}) \]
Step 5: Multiply.
\[ q_{in} = 70.8\times10^{-9}\ \text{C} \]
Step 6: Convert to nanocoulombs.
Since $10^{-9}$ C is one nanocoulomb: \[ \boxed{q_{in} \approx 70\ \text{nC}} \]