Five charges $q_{1}, q_{2}, q_{3}, q_{4}$ and $q_{5}$ are fixed at their positions as shown $S$ is Gaussian surface. The Gauss's law is given by $\oint_{S} \vec{E} \cdot \vec{d S} = \frac{q}{ε_{0}} .$ Which of the following statements is correct?

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$\vec{E}$ on the LHS of the above equation will have a contribution from $q_{1}, q_{5}$ and $q_{3}$ while $q$ on the RHS will have a contribution from $q_{2}$ and $q_{4}$ only.

$\vec{E}$ on the LHS of the above equation will have a contribution from all charges while $q$ on the RHS will have a contribution from $q_{2}$ and $q_{4}$ only.

$\vec{E}$ on the LHS of the above equation will have a contribution from all charges while $q$ on the RHS will have a contribution from from $q_{1}, q_{3}$ and $q_{5}$ only.

Both $\vec{E}$ on the LHS and $q$ on the RHS will have a contribution from from $q_{2}$ and $q_{4}$ only..

answer is B.

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Detailed Solution

$\vec{E}$ on the LHS of the above equation will have a contribution from all charges while $q$ because it is the flux of the net electric field, whereas on the RHS ‘q’ will have a contribution from $q_{2}$ and $q_{4}$ only(i.e; charge enclosed by the gaussian surface).

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