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General

General

Easy

Question

q₁, q₂ , q₃ and q₄ 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?

$∮_{s} ({\vec{E}}_{1} + {\vec{E}}_{2} + {\vec{E}}_{3}) \cdot d \vec{A} = \frac{q_{1} + q_{2} + q_{3}}{2 ε_{0}}$
$∮_{s} ({\vec{E}}_{1} + {\vec{E}}_{2} + {\vec{E}}_{3}) \cdot d \vec{A} = \frac{(q_{1} + q_{2} + q_{3})}{ε_{0}}$
$∮_{s} ({\vec{E}}_{1} + {\vec{E}}_{2} + {\vec{E}}_{3}) \cdot d \vec{A} = \frac{(q_{1} + q_{2} + q_{3} + q_{4})}{ε_{0}}$
None of these

The correct answer is: $text ∮ end text blank subscript straight s open parentheses straight E with rightwards arrow on top subscript 1 plus straight E with rightwards arrow on top subscript 2 plus straight E with rightwards arrow on top subscript 3 close parentheses times straight d straight A with rightwards arrow on top equals fraction numerator open parentheses straight q subscript 1 plus straight q subscript 2 plus straight q subscript 3 close parentheses over denominator epsilon subscript 0 end fraction$

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