Match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| (Maxwell’s Equations) | (Laws) | ||
| (A) | \( \displaystyle\oint \mathbf{E}.d\mathbf{A} = \frac{Q_{enc}}{\varepsilon_{0}} \) | (I) | Gauss’s law for Magnetism |
| (B) | \( \displaystyle\oint \mathbf{B}.d\mathbf{A} = 0 \) | (II) | Faraday’s Law |
| (C) | \( \displaystyle\oint \mathbf{E}.d\mathbf{l} = -\frac{d\phi_{B}}{dt} \) | (III) | Ampere-Maxwell Law |
| (D) | \( \displaystyle\oint \mathbf{B}.d\mathbf{l} = \mu_{0}\varepsilon_{0}\frac{d\phi_{E}}{dt} + \mu_{0}i_{c} \) | (IV) | Gauss’s law for Electricity |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A) - (IV), (B) - (I), (C) - (II), (D) - (III)
The four Maxwell’s equations in integral form are the laws of Gauss (for electric and for magnetic fields), Faraday and Ampere-Maxwell. Identify each by what it integrates: a field over a closed surface (dA) or a field around a closed loop (dl).
(A) \( \oint \mathbf{E}.d\mathbf{A} = Q_{enc}/\varepsilon_{0} \) — this matches (IV) Gauss’s law for Electricity. The electric flux through a closed surface is set by the enclosed charge.
(B) \( \oint \mathbf{B}.d\mathbf{A} = 0 \) — this matches (I) Gauss’s law for Magnetism. The magnetic flux through any closed surface is zero because isolated magnetic poles do not exist.
(C) \( \oint \mathbf{E}.d\mathbf{l} = -d\phi_{B}/dt \) — this matches (II) Faraday’s Law. The emf round a loop equals the rate of change of the magnetic flux through it.
(D) \( \oint \mathbf{B}.d\mathbf{l} = \mu_{0}\varepsilon_{0}\,d\phi_{E}/dt + \mu_{0}i_{c} \) — this matches (III) Ampere-Maxwell Law. The conduction current together with the displacement current produces the magnetic field round a loop.
Note: A similar question was also asked in CUET (UG) 2026 on 18-05-2026 (Slot 1), and in CUET (UG) 2023 on 13-06-2023 (Slot 2) and on 26-05-2023 (Slot 1).
NCERT (2026-27):
Displacement Current – “… MAXWELL’S EQUATIONS IN VACUUM
\( \displaystyle 1.\ \oint \mathbf{E}\cdot d\mathbf{A} = Q/\varepsilon_0 \)
(Gauss’s Law for electricity)
\( \displaystyle 2.\ \oint \mathbf{B}\cdot d\mathbf{A} = 0 \)
(Gauss’s Law for magnetism)
\( \displaystyle 3.\ \oint \mathbf{E}\cdot d\mathbf{l} = -\frac{d\Phi_B}{dt} \)
(Faraday’s Law)
\( \displaystyle 4.\ \oint \mathbf{B}\cdot d\mathbf{l} = \mu_0 i_c + \mu_0 \varepsilon_0 \frac{d\Phi_E}{dt} \)
(Ampere – Maxwell Law)”