Question

Shown below is a distribution of charges. The flux of electric field due to these charges through the surface $S$ is

• A. $\frac{3 q}{\varepsilon_{0}}$
• B. $\frac{2 q}{\varepsilon_{0}}$
• C. $\frac{q}{\varepsilon_{0}}$
• D. zero

Answer 1

Answer: (D)

According to Gauss's theorem, the electric flux through any closed surface is equal to $1 / \varepsilon_{0}$ times the net charge $q$ enclosed by the surface, that is
$\phi_{E}=\oint \vec{E} \cdot d \vec{A}=\frac{q}{\varepsilon_{0}}$
Since total charge enclosed by surface is zero,
$\therefore $ Total electric flux, $\phi=0$