Match List-I with List-II
| List-I | List-II |
| Maxwell’s Equations in Vacuum (Left part) | Maxwell’s Equations in Vacuum (Right part) |
| (A) \( \oint \vec{B}\cdot d\vec{l} \) | (I) \( -\,(d\Phi_{B}/dt) \) |
| (B) \( \oint \vec{E}\cdot d\vec{A} \) | (II) 0 |
| (C) \( \oint \vec{E}\cdot d\vec{l} \) | (III) \( Q/\varepsilon_{0} \) |
| (D) \( \oint \vec{B}\cdot d\vec{A} \) | (IV) \( \mu_{0} i_{c} + \mu_{0}\varepsilon_{0}\,(d\Phi_{E}/dt) \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A) - (IV), (B) - (III), (C) - (I), (D) - (II)
The four Maxwell's equations in vacuum give the closed-loop and closed-surface integrals of \( \vec{E} \) and \( \vec{B} \).
(A) \( \oint \vec{B}\cdot d\vec{l} \) — this matches (IV) \( \mu_{0} i_{c} + \mu_{0}\varepsilon_{0}\,d\Phi_{E}/dt \). This is the Ampere-Maxwell law: the circulation of \( \vec{B} \) is due to the conduction current and the displacement current.
(B) \( \oint \vec{E}\cdot d\vec{A} \) — this matches (III) \( Q/\varepsilon_{0} \). This is Gauss's law for electricity.
(C) \( \oint \vec{E}\cdot d\vec{l} \) — this matches (I) \( -\,d\Phi_{B}/dt \). This is Faraday's law: a changing magnetic flux produces a circulating electric field.
(D) \( \oint \vec{B}\cdot d\vec{A} \) — this matches (II) 0. This is Gauss's law for magnetism: there are no magnetic monopoles, so the net magnetic flux through a closed surface is zero.
NCERT (2026-27):
Maxwell’s Equations in Vacuum – “1. \( \oint \mathbf{E}\cdot d\mathbf{A} = Q/\varepsilon_0 \) (Gauss’s Law for electricity)
2. \( \oint \mathbf{B}\cdot d\mathbf{A} = 0 \) (Gauss’s Law for magnetism)
3. \( \oint \mathbf{E}\cdot d\mathbf{l} = -\frac{d\Phi_B}{dt} \) (Faraday’s Law)
4. \( \oint \mathbf{B}\cdot d\mathbf{l} = \mu_0 i_c + \mu_0\varepsilon_0\frac{d\Phi_E}{dt} \) (Ampere – Maxwell Law)”