Question: Q. 6. Fivecharges $q_{1}, q_{2}, q_{3}, q_{4}$, and $q_{5}$ are fixed at their posifions as shown in Figure. $S$ is a Gaussian surface. The Gauss’s law is given by :
$$ \oint_{s} E . d s=\frac{q}{\varepsilon_{0}} $$
Gaussian Surface
Which of the following statements is correct?
(a) $E$ 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) $E$ 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) $E$ on the LHS of the above equation will have a contribution from all charges while $q$ on the RHS will have a contribution from $q_{1}, q_{3}$ and $q_{5}$ only.
(d) Both $E$ on the LHS and $q$ on the RHS will have contributions from $q_{2}$ and $q_{4}$ only.
[NCERT Exemplar]
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Solution:
Ans. Correct option : (b)
Explanation : As all charges are positive (or of same signs) so electric field lines on R.H.S. of Gaussian surface will be due to $q_{2}$ and $q_{4}$ only.
On L.H.S. of Gaussian surface, the electric field lines on ’ $E$ ’ will be due to $q_{1}, q_{2}, q_{3}, q_{4}$ and $q_{5}$. So, answer $(b)$ is verified.
