A point charge of \( 17.7\,\mu\mathrm{C} \) is located at the center of a cube of side 0.03 m. Find the electric flux through each face of the cube.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 3.3 \times 10^{5}\,\mathrm{N\,m^2\,C^{-1}} \)
By Gauss's law, the total flux through the closed surface of the cube is \( q/\varepsilon_0 \). The charge sits at the centre, so by symmetry the six faces share this flux equally.
\( \displaystyle \Phi_{\text{face}} = \frac{q}{6\,\varepsilon_0} \)
\( q = 17.7\,\mu\mathrm{C} = 17.7\times10^{-6}\,\mathrm{C} \)
\( \varepsilon_0 = 8.85\times10^{-12}\,\mathrm{C^2\,N^{-1}\,m^{-2}} \)
\( \displaystyle \Phi_{\text{face}} = \frac{17.7\times10^{-6}}{6 \times 8.85\times10^{-12}} = \frac{17.7\times10^{-6}}{53.1\times10^{-12}} = 3.3\times10^{5}\,\mathrm{N\,m^2\,C^{-1}} \)