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

Easy

A

$\oint_{S} ({\vec{E}}_{1} + {\vec{E}}_{2} + {\vec{E}}_{3}) . d \vec{A} = \frac{q_{1} + q_{2} + q_{3}}{2 ε_{o}}$
B

$\oint_{S} ({\vec{E}}_{1} + {\vec{E}}_{2} + {\vec{E}}_{3} + {\vec{E}}_{4}) . d \vec{A} = \frac{(q_{1} + q_{2} + q_{3})}{ε_{o}}$
C

$\oint_{S} ({\vec{E}}_{1} + {\vec{E}}_{2} + {\vec{E}}_{3}) . d \vec{A} = \frac{q_{1} + q_{2} + q_{3} + q_{4}}{2 ε_{o}}$
D

None of the above

Solution

According to Gauss's Law, $\int \vec{E} . d \vec{A} = \frac{1}{ε_{o}} (Q_{enc})$
Here, resultant electric field is due to all the charges present outside or inside the Gaussian surface but net charge appearing in the law is taken as the charges enclosed by the surface.

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