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Gauss's Law

q1, q2, q3 an...

Question

$q_{1}, q_{2}, q_{3} a n d q_{4}$ are point charges located at points as shown in the figure and S is spherical Gaussian surface of radius R. Which of the following is true according to the Gauss’s law.

A

\oint ({\to E}_{1} + {\to E}_{2} + {\to E}_{3}) . d \to A = \frac{q_{1} + q_{2} + q_{3}}{2 ϵ_{0}}

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B

\oint ({\to E}_{1} + {\to E}_{2} + {\to E}_{3}) . d \to A = \frac{q_{1} + q_{2} + q_{3}}{ϵ_{0}}

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C

\oint ({\to E}_{1} + {\to E}_{2} + {\to E}_{3}) . d \to A = \frac{q_{1} + q_{2} + q_{3} + q_{4}}{ϵ_{0}}

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D

N o n e o f t h e a b o v e

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Solution

The correct option is B $\oint ({\to E}_{1} + {\to E}_{2} + {\to E}_{3}) . d \to A = \frac{q_{1} + q_{2} + q_{3}}{ϵ_{0}}$
$\oint ({\to E}_{1} + {\to E}_{2} + {\to E}_{3}) . d \to A = \frac{q_{1} + q_{2} + q_{3}}{ϵ_{0}}$
$q_{4}$ is outside the closed path.

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