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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-IList-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

  1. A a - ii, b - i, c – iii
  2. B a - iii, b - ii, c – i
  3. C a - i, b - ii, c – iii
  4. D a - ii, b - iii, c – i
Verified Solution

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