Match List-I with List-II (the symbols carry their usual meaning).

**List-I**
(A) $\oint \vec{E} \cdot d\vec{

Question

Match List-I with List-II (the symbols carry their usual meaning).

**List-I**
(A) $\oint \vec{E} \cdot d\vec{A} = \frac{Q}{\varepsilon_0}$
(B) $\oint \vec{B} \cdot d\vec{A} = 0$
(C) $\oint \vec{E} \cdot d\vec{l} = -\frac{d\phi}{dt}$
(D) $\oint \vec{B} \cdot d\vec{l} = \mu_0 i_c + \mu_0 \varepsilon_0 \frac{d\phi_E}{dt}$

**List-II**
(I) Ampere-Maxwell's law
(II) Faraday's law
(III) Gauss's law of electrostatics
(IV) Gauss's law of magnetism

Accepted Answer

1. **Equation A:** $\oint \vec{E} \cdot d\vec{A} = Q/\varepsilon_0$ represents the total electric flux through a closed surface being proportional to the enclosed charge. This is **Gauss's Law of Electrostatics** (III).
2. **Equation B:** $\oint \vec{B} \cdot d\vec{A} = 0$ indicates that the net magnetic flux through any closed surface is zero, implying magnetic monopoles do not exist. This is **Gauss's Law of Magnetism** (IV).
3. **Equation C:** $\oint \vec{E} \cdot d\vec{l} = -d\phi/dt$ describes how a time-varying magnetic flux induces an electric field. This is **Faraday's Law of Induction** (II).
4. **Equation D:** $\oint \vec{B} \cdot d\vec{l} = \mu_0 i_c + \mu_0 \varepsilon_0 \frac{d\phi_E}{dt}$ is the generalized form of Ampere's Circuital Law, including the displacement current term introduced by Maxwell. This is the **Ampere-Maxwell Law** (I).
Therefore, the correct matching sequence is A-III, B-IV, C-II, D-I.

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