Question

The inward and outward electric flux for a closed surface in units of $M{m}^2/C$ are respectively $8\times {10}^3$ and $4\times {10}^3$. Then the total charge inside the surface in S.I units is :

(where ${\epsilon }_0$ = permittivity constant )

• A. $4\times {10}^3$
• B. $-4\times {10}^3$
• C. $-\frac{\pi R^2-\pi R}{E}$
• D. $-4\times {10}^3{\epsilon }_0$

Answer 1

The correct option is D $-4\times {10}^3{\epsilon }_0$

Given,

${\varphi }_i=-8\times {10}^{3}N{m}^2/C$ (inward direction)

${\varphi }_o=4\times {10}^{3}N{m}^2/C$ (outward direction)

Electric flux is given by Gauss's law,

$\varphi =\frac{Q\left(enclosed\right)}{{\epsilon }_0}$

$Q\left(enclosed\right)=({\varphi }_i+{\varphi }_o){\epsilon }_0$

$Q\left(enclosed\right)=(-8\times {10}^3+4\times {10}^3){\epsilon }_0$

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

The correct option is D.