Question

Five charges $q_1$, $q_2$, $q_3$, $q_4$ and $q_5$ are fixed at their positions as shown in figure. $S$ is Gaussian surface. The Gauss’s law is given by ${\oint }_{{}_{{}_s}}\vec{E}\cdot \overrightarrow{ds}=\frac{q}{{\epsilon }_0}$. Which of the following statements is correct?

• A. $\vec{E}$ 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
• B. $\vec{E}$ 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
• C. $\vec{E}$ on the $LHS$ of the above equation will have a contribution from all charges while q on the $RHS$ will have a contribution from qly $q_3$ and $q_5$ only
• D. Both $\vec{E}$ on the $LHS$ and $q$ on the $RHS$ will have a contributions from $q_2$ and $q_4$ only

Answer 1

Answer: (B)

Key concept : According to Gauss' law, the term $q_{\text{enclosed}}$ on the right side of the equation ${\varphi }_{s}E.dS=q_{\text{enclosed }/i{n}_0}$ includes the sum of all charges enclosed by the surface called (Gaussian surface).
In left side equation, the electric field is due to all the charges present both inside as well as outside the Gaussian surface.
Hence in given question, $E$ on 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. Hence option (b) is correct.