JEE Main 2024 · 29 January · morning · Single correct · +4 / −1
Match List I with List II
Choose the correct answer from the options given below:
| List - I | List - II | ||
|---|---|---|---|
| (A) | ∮ B⃗ · d l⃗=μₒ i_c+μₒ εₒ (d φ_E)/(d t) | (I) | Gauss' law for electricity |
| (B) | ∮ E⃗ · d l⃗=(d φ_B)/(d t) | (II) | Gauss' law for magnetism |
| (C) | ∮ E⃗ · d A⃗=Q/εₒ | (III) | Faraday law |
| (D) | ∮ B⃗ · d A⃗=0 | (IV) | Ampere - Maxwell law |
- (a) A-IV, B-III, C-I, D-II
- (b) A-I, B-II, C-III, D-IV
- (c) A-IV, B-I, C-III, D-II
- (d) A-II, B-III, C-I, D-IV
Answer and solution
Answer (a) A-IV, B-III, C-I, D-II
Solution
Physics sir · 4 steps
Ask two things of each equation: which field is inside, and is it a loop or a closed surface?
- Loop or surface. An integral with dl⃗ goes round a closed loop. Faraday's law and the Ampere-Maxwell law are loop laws. An integral with dA⃗ is a flux through a closed surface, and the two Gauss laws are surface laws.
- Which field. A loop law for E⃗ links it to a changing magnetic flux, which is Faraday's law. A loop law for B⃗ links it to currents, which is the Ampere-Maxwell law. For the closed surfaces, E⃗ flux equals enclosed charge over ε₀, while B⃗ flux is zero.
Equation Integral of Right-hand side Law (A) B⃗ round a loop conduction current plus displacement current Ampere-Maxwell (IV) (B) E⃗ round a loop rate of change of φ_B Faraday (III) (C) E⃗ over a closed surface Q/ε₀ Gauss for electricity (I) (D) B⃗ over a closed surface 0 Gauss for magnetism (II) - A note on B. The usual form of Faraday's law has a minus sign: ∮ E⃗ · dl⃗ = -dφ_B/dt. That sign is Lenz's law. The question leaves it out, but a loop integral of E⃗ against a changing φ_B can only be Faraday's law.
- So. The matching is A-IV, B-III, C-I, D-II, which is option (a).
The idea to keep. Closed surface (dA⃗) means a Gauss law. Closed loop (dl⃗) means Faraday or Ampere-Maxwell. Then the field inside the integral tells you which one it is.
Answer from the NTA final answer key. Solution by PrepWiser.