Discussion
The inward and outward electric flux from a closed surface are \(6 \times 10^{4}NM^{2}C^{-1}\) and \(3 \times 10^{4}NM^{2}C^{-1}\). Then the net charge (in coulomb) inside the closed surface is
Answer: E
The net charge is \(-3 \times 10^{4}\varepsilon_{0}\) C.
Outward flux counts as positive and inward flux as negative, so the net flux is
\[ \begin{aligned} \Phi &= 3 \times 10^{4} - 6 \times 10^{4} = -3 \times 10^{4}\ \text{N m}^{2}\text{C}^{-1} \\ q &= \varepsilon_{0}\Phi = -3 \times 10^{4}\varepsilon_{0} \end{aligned} \]
by Gauss's law, \(\Phi = \frac{q}{\varepsilon_{0}}\). More flux entering than leaving means a net negative charge inside. \(9 \times 10^{4}\varepsilon_{0}\) adds the fluxes, and \(\pm 6 \times 10^{4}\varepsilon_{0}\) uses only the inward flux.
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