Five charges \(q_1, q_2, q_3, q_4~\text{and}~q_5\) are fixed at their positions as shown in the figure, \(S\) is a Gaussian surface. The Gauss' law is given by \(\int_{S}E\cdot dS= \frac{q}{\varepsilon_0}\). Which of the following statements is correct?
| 1. | \(E\) on the LHS of the above equation will have contribution from \(q_1, q_5~\text{and}~q_3\) while \(q\) on the RHS will have a contribution from \(q_2~\text{and}~q_4\) only. |
| 2. | \(E\) on the LHS of the above equation will have a contribution from all charges while \(q\) on the RHS will have a contribution from \(q_2~\text{and}~q_4\) only. |
| 3. | \(E\) on the LHS of the above equation will have a contribution from all charges while \(q\) on the RHS will have a contribution from \(q_1, q_3~\text{and}~q_5\) only. |
| 4. | Both \(E\) on the LHS and \(q\) on the RHS will have contributions from \(q_2\) and \(q_4\) only. |
Hint: Use Gauss' law.
Step 1: According to Gauss' law, the term q on the right side of the equation includes the sum of all charges enclosed by the surface.
Step 2: The charges may be located anywhere inside the surface, if the surface is so chosen that there are some charges inside and some outside, the electric field on the left side of the equation is due to all the charges, both inside and outside S.
So, E on LHS of the above equation will have a contribution from all charges while q on the RHS will have a contribution from q2 and q4 only.
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