KCET · Physics · Electrostatics
Consider three point charges \(-2Q, Q\) and \(-Q\) and three surfaces \(S_1, S_2\) and \(S_3\) as shown in the figure. Match the entries of List-I with that of List-II.

| List-I | List-II |
|---|---|
| (a) Net flux through \(S_1\) | (i) \(\dfrac{-2Q}{\varepsilon_0}\) |
| (b) Net flux through \(S_2\) | (ii) \(\dfrac{-Q}{\varepsilon_0}\) |
| (c) Net flux through \(S_3\) | (iii) Zero |
- A a - ii, b - i, c – iii
- B a - iii, b - ii, c – i
- C a - i, b - ii, c – iii
- D a - ii, b - iii, c – i
Answer & Solution
Correct Answer
(D) a - ii, b - iii, c – i
Step-by-step Solution
Detailed explanation
According to Gauss's Law, the net electric flux through any closed surface is given by \(\Phi = \dfrac{Q_{\text{enclosed}}}{\varepsilon_0}\).
For surface \(S_1\), the enclosed charges are \(-2Q\) and \(Q\).
Net charge enclosed by \(S_1 = -2Q + Q = -Q\).
Net flux through \(S_1 = \dfrac{-Q}{\varepsilon_0}\).
Thus, (a) matches with (ii).
For surface \(S_2\), the enclosed charges are \(Q\) and \(-Q\).
Net charge enclosed by \(S_2 = Q + (-Q) = 0\).
Net flux through \(S_2 = 0\).
Thus, (b) matches with (iii).
For surface \(S_3\), the enclosed charges are \(-2Q\), \(Q\), and \(-Q\).
Net charge enclosed by \(S_3 = -2Q + Q + (-Q) = -2Q\).
Net flux through \(S_3 = \dfrac{-2Q}{\varepsilon_0}\).
Thus, (c) matches with (i).
The correct matching is a - ii, b - iii, c - i.
Answer: a - ii, b - iii, c – i
For surface \(S_1\), the enclosed charges are \(-2Q\) and \(Q\).
Net charge enclosed by \(S_1 = -2Q + Q = -Q\).
Net flux through \(S_1 = \dfrac{-Q}{\varepsilon_0}\).
Thus, (a) matches with (ii).
For surface \(S_2\), the enclosed charges are \(Q\) and \(-Q\).
Net charge enclosed by \(S_2 = Q + (-Q) = 0\).
Net flux through \(S_2 = 0\).
Thus, (b) matches with (iii).
For surface \(S_3\), the enclosed charges are \(-2Q\), \(Q\), and \(-Q\).
Net charge enclosed by \(S_3 = -2Q + Q + (-Q) = -2Q\).
Net flux through \(S_3 = \dfrac{-2Q}{\varepsilon_0}\).
Thus, (c) matches with (i).
The correct matching is a - ii, b - iii, c - i.
Answer: a - ii, b - iii, c – i
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