First slide

Gauss's Law

Question

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

Moderate

A

$\frac{3 q}{ε_{0}}$
B

$\frac{2 q}{ε_{0}}$
C

$\frac{q}{ε_{0}}$
D

Zero

Solution

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

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