Question

The inward and outward electric flux for a closed surface in units of $N - m ^{2} / C$ are respectively $8 \times 10^{3}$ and $4 \times 10^{3}$. Then the total charge inside the surface is (where $\varepsilon_{0}=$ permittivity constant)

• A. $4 \times 10^{3} C$
• B. $-4 \times 10^{3} C$
• C. $\frac{\left(-4 \times 10^{3}\right)}{\varepsilon_{0}} C$
• D. $-4 \times 10^{3} \varepsilon_{0} C$

Answer 1

Answer: (D)

By Gauss's law, $\phi=\frac{1}{\varepsilon_{0}}\left(Q_{\text {enclosed }}\right)$
$\Rightarrow Q_{\text {enclosed }}=\phi \varepsilon_{0}=\left(-8 \times 10^{3}+4 \times 10^{3}\right) \varepsilon_{0}$
$=-4 \times 10^{3} \varepsilon_{0}$ C.