For Maxwell's Equations in Vacuum, match List-I with List-II
| List-I- (Physical Laws) | List-II (Integral Representations) | ||
| (A) | Faraday's Law | (I) | \( \oint E.dA = Q/\epsilon_0 \) |
| (B) | Ampere-Maxwell Law | (II) | \( \oint B.dA = 0 \) |
| (C) | Gauss's Law for magnetism | (III) | \( \oint E.dl = -d\phi_B/dt \) |
| (D) | Gauss's Law for Electricity | (IV) | \( \oint B.dl = \mu_0 i_c + \mu_0\epsilon_0 (d\phi_E)/dt \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A) - (III), (B) - (IV), (C) - (II), (D) - (I)
Each of Maxwell’s equations is recognised by what is integrated (E or B) and over what (a closed surface dA or a closed loop dl).
(A) Faraday's Law — this matches (III) \( \oint E.dl = -d\phi_B/dt \). The emf round a loop equals the negative rate of change of magnetic flux.
(B) Ampere-Maxwell Law — this matches (IV) \( \oint B.dl = \mu_0 i_c + \mu_0\epsilon_0 (d\phi_E)/dt \). The line integral of B depends on the conduction current plus the displacement current.
(C) Gauss's Law for magnetism — this matches (II) \( \oint B.dA = 0 \). There are no magnetic monopoles, so the net magnetic flux through a closed surface is zero.
(D) Gauss's Law for Electricity — this matches (I) \( \oint E.dA = Q/\epsilon_0 \). The electric flux through a closed surface is the enclosed charge divided by \( \epsilon_0 \).
Note: A similar question was also asked in CUET (UG) 2026 on 21-05-2026 (Slot 1), and in CUET (UG) 2023 on 13-06-2023 (Slot 2) and on 26-05-2023 (Slot 1).
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. \( \oint \mathbf{E}\cdot d\mathbf{l} = \dfrac{-d\Phi_B}{dt} \) (Faraday’s Law)
4. \( \oint \mathbf{B}\cdot d\mathbf{l} = \mu_0 i_c + \mu_0 \varepsilon_0 \dfrac{d\Phi_E}{dt} \) (Ampere – Maxwell Law)”