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):
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):
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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.
Updated On: Jun 8, 2026
- 70 nC
- 42 nC
- 21 nC
- 60 nC
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The Correct Option is A
Solution and Explanation
Concept:
According to Gauss's Law in electrostatics, the net total electric flux \( \phi \) emerging outward through any closed Gaussian surface enclosing a region is directly proportional to the total net enclosed electric charge \( q_{\text{in}} \):
\[
\phi = \frac{q_{\text{in}}}{\varepsilon_0} \implies q_{\text{in}} = \phi \cdot \varepsilon_0
\]
where \( \varepsilon_0 = 8.854\times10^{-12}~\text{C}^2\text{N}^{-1}\text{m}^{-2} \) is the permittivity constant of free space.
Step 1: Substituting given numbers into Gauss's equation.
Given value for outward total flux: \( \phi = 8.0\times10^3~\text{Nm}^2\text{C}^{-1} \). \[ q_{\text{in}} = (8.0\times10^3) \times (8.854\times10^{-12}) \]
Step 2: Calculating the enclosed charge value.
\[ q_{\text{in}} = 70.832\times10^{-9}~\text{C} = 70.832~\text{nC} \approx 70~\text{nC} \] Thus, the net charge inside the box is approximately 70 nC.
Step 1: Substituting given numbers into Gauss's equation.
Given value for outward total flux: \( \phi = 8.0\times10^3~\text{Nm}^2\text{C}^{-1} \). \[ q_{\text{in}} = (8.0\times10^3) \times (8.854\times10^{-12}) \]
Step 2: Calculating the enclosed charge value.
\[ q_{\text{in}} = 70.832\times10^{-9}~\text{C} = 70.832~\text{nC} \approx 70~\text{nC} \] Thus, the net charge inside the box is approximately 70 nC.
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