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 $[\text{where}{\epsilon }_0=\text{permittivity constant}]$

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

Answer 1

The correct option is D $-4\times {10}^3{\epsilon }_{0}C$

Given:

Incoming flux $=-8\times {10}^{3}N{m}^2{C}^{-}1$
and

outgoing flux $=4\times {10}^{3}N{m}^2{C}^{-}1$

Net Incoming flux

$=(-8+4)\times {10}^3=-4\times {10}^{3}N{m}^2{C}^{-}1$

According to the Gauss law net flux,

${\varphi }_{\text{net}}=\frac{Q_{\text{inside}}}{{\epsilon }_0}$

$q=\left(\text{net incoming flux}\right){\epsilon }_0$

$q=-4\times {10}^3{\epsilon }_{0}C$