First slide

Gauss's law and its applications

Question

Figure shows four charges q₁, q₂, q₃, and q₄ fixed in space. Then the total flux of the electric field through a closed surface S, due to all the charges, is

Moderate

A

not equal to the total flux through S due to q₃ and q₄
B

equal to the total flux through S due to q₃ and q₄
C

zero if $q_{1} + q_{2} = q_{3} + q_{4}$
D

twice the total flux through S due to q₃ and q₄ if q₁+q₂=q₃+q₄

Solution

Net flux is due to charges inside S only.
$ϕ = \frac{q_{3} + q_{4}}{ε_{0}}$

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