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 ${\epsilon }_0=$ permittivity constant)

• A. $4\times 10^{3}C$
• B. $-4\times 10^{3}C$
• C. $\frac{\left(-4\times 10^3\right)}{{\epsilon }_0}C$
• D. $-4\times 10^3{\epsilon }_{0}C$

Answer 1

Answer: (D)

By Gauss's law, $\varphi =\frac{1}{{\epsilon }_0}\left(Q_{\text{enclosed }}\right)$
$\Rightarrow Q_{\text{enclosed }}=\varphi {\epsilon }_0=\left(-8\times 10^3+4\times 10^3\right){\epsilon }_0$
$=-4\times 10^3{\epsilon }_0$ C.