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Electromagnetic Induction question

2024 · 30 Jan · Shift 2 · Q69
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Electromagnetic Induction question

2024 · 30 Jan · Shift 2 · Q69

JEE MainPhysicsElectromagnetic InductionMCQ+4 / −1

Match List I with List II

List I List II
(A) Gauss's law of magnetostatics (I) ∮E⃗⋅d⃗a=1ε0∫ρdV\oint \vec{E} \cdot \vec{d} a=\frac{1}{\varepsilon_0} \int \rho d V∮E⋅da=ε0​1​∫ρdV
(B) Faraday's law of electro magnetic induction (II) ∮B⃗⋅d⃗a=0\oint \vec{B} \cdot \vec{d} a=0∮B⋅da=0
(C) Ampere's law (III) ∫E⃗⋅d⃗l=−ddt∫B⃗⋅d⃗a\int \vec{E} \cdot \vec{d} l=\frac{-d}{d t} \int \vec{B} \cdot \vec{d} a∫E⋅dl=dt−d​∫B⋅da
(D) Gauss's law of electrostatics (IV) ∮B⃗⋅d⃗l=μ0I\oint \vec{B} \cdot \vec{d} l=\mu_0 I∮B⋅dl=μ0​I

Choose the correct answer from the options given below:

  1. A
    A-III, B-IV, C-I, D-II
  2. B
    A-IV, B-II, C-III, D-I
  3. C
    A-II, B-III, C-IV, D-I
  4. D
    A-I, B-III, C-IV, D-II
View written solutionFree

Correct answer: C

  1. Identify each law and its mathematical form

    We match each item in List I with the corresponding equation in List II.

  2. Match (A) Gauss's law of magnetostatics

    Gauss's law for magnetism states that the net magnetic flux through any closed surface is zero: ∮B⃗⋅d⃗a=0\oint \vec{B}\cdot \vec{d}a = 0∮B⋅da=0 This corresponds to (II).

  3. Match (B) Faraday's law of electromagnetic induction

    Faraday's law states: ∮E⃗⋅d⃗l=−ddt∫B⃗⋅d⃗a\oint \vec{E}\cdot \vec{d}l = -\frac{d}{dt}\int \vec{B}\cdot \vec{d}a∮E⋅dl=−dtd​∫B⋅da This corresponds to (III).

  4. Match (C) Ampere's law

    Ampere's circuital law is: ∮B⃗⋅d⃗l=μ0I\oint \vec{B}\cdot \vec{d}l = \mu_0 I∮B⋅dl=μ0​I This corresponds to (IV).

  5. Match (D) Gauss's law of electrostatics

    Gauss's law in electrostatics is: ∮E⃗⋅d⃗a=1ε0∫ρ dV\oint \vec{E}\cdot \vec{d}a = \frac{1}{\varepsilon_0}\int \rho\, dV∮E⋅da=ε0​1​∫ρdV This corresponds to (I).

  6. Final matching

    A→II,B→III,C→IV,D→IA \to II, \quad B \to III, \quad C \to IV, \quad D \to IA→II,B→III,C→IV,D→I

  7. Compare with options

    This matches Option C.

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