JEE Main 2024 · 30 January · evening · Single correct · +4 / −1
Match List I with List II
Choose the correct answer from the options given below:
| List I | List II | ||
|---|---|---|---|
| (A) | Gauss's law of magnetostatics | (I) | ∮ E⃗ · d⃗ a=1/ε₀ ∫ ρ d V |
| (B) | Faraday's law of electro magnetic induction | (II) | ∮ B⃗ · d⃗ a=0 |
| (C) | Ampere's law | (III) | ∫ E⃗ · d⃗ l=-d/(d t) ∫ B⃗ · d⃗ a |
| (D) | Gauss's law of electrostatics | (IV) | ∮ B⃗ · d⃗ l=μ₀ I |
- (a) A-III, B-IV, C-I, D-II
- (b) A-IV, B-II, C-III, D-I
- (c) A-II, B-III, C-IV, D-I
- (d) A-I, B-III, C-IV, D-II
Answer and solution
Answer (c) A-II, B-III, C-IV, D-I
Solution
Physics sir · 3 steps
Look at what each integral is over: a closed surface means Gauss, a closed loop means Faraday or Ampere.
- Surface integrals. A closed-surface integral ∮ · da⃗ is a flux through a closed surface, so it is a Gauss's law. Flux of E⃗ equals enclosed charge over ε₀ (electrostatics). Flux of B⃗ is always zero because there are no magnetic monopoles (magnetostatics).
- Line integrals. A line integral ∫ · dl⃗ around a loop is a circulation. Circulation of E⃗ equals minus the rate of change of magnetic flux (Faraday). Circulation of B⃗ equals μ₀ I (Ampere).
Law Integral type Matching equation (A) Gauss, magnetostatics flux of B⃗ (II) ∮ B⃗ · da⃗ = 0 (B) Faraday circulation of E⃗ (III) ∮ E⃗ · dl⃗ = -d/dt∫ B⃗ · da⃗ (C) Ampere circulation of B⃗ (IV) ∮ B⃗ · dl⃗ = μ₀ I (D) Gauss, electrostatics flux of E⃗ (I) ∮ E⃗ · da⃗ = 1/ε₀∫ ρ dV - So. The matching is A-II, B-III, C-IV, D-I, which is option (c).
The idea to keep. Maxwell's four laws pair up neatly: two fluxes (Gauss for E⃗ and B⃗) and two circulations (Faraday for E⃗, Ampere for B⃗). Spot the integral type and the field, and the law follows.
Answer from the NTA final answer key. Solution by PrepWiser.