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Equipotential Surfaces

q1, q2, q3 an...

Question

$q_{1}, q_{2}, q_{3}$ 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 ?

A

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

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B

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

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C

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

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D

\oint (_{1} +_{2} +_{3}) . - \to d A = q_{1} + q_{2} + q_{3}

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Solution

The correct option is B $\oint (_{1} +_{2} +_{3} +_{4}) . - \to d A = \frac{q_{1} + q_{2} + q_{3}}{ε_{0}}$
The Gaussiam Surface encloses only the point charges $q_{1}, q_{2}$ and $q_{3}$ . The charge $q_{4}$ is outside the Gaussian surface.

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

 Hence, (b) is the correct answer.

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