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MCQEasyJEE 2024Faraday's Laws of EMI

JEE Physics 2024 Question with Solution

Match List I with List II: List I: A. Gauss’s Law B. Faraday’s Law C. Lenz’s Law D. Ampere’s Law

List II: I. ∮E⃗⋅dA=Qε0\oint \vec{E} \cdot dA = \frac{Q}{\varepsilon_0} II. ∮B⃗⋅dl⃗=μ0I\oint \vec{B} \cdot d\vec{l} = \mu_0 I III. Induced emf opposes change IV. ∮E⃗⋅dl⃗=−dΦdt\oint \vec{E} \cdot d\vec{l} = -\frac{d\Phi}{dt}

  • A

    A - I, B - IV, C - III, D - II

  • B

    A - IV, B - I, C - III, D - II

  • C

    A - II, B - III, C - IV, D - I

  • D

    A - I, B - II, C - IV, D - III

Answer

Correct answer:A

Step-by-step solution

Standard Method

Given: List I contains the laws Gauss’s Law, Faraday’s Law, Lenz’s Law, and Ampere’s Law. List II contains their corresponding equations or statements.

Find: The correct matching between List I and List II.

Gauss’s Law corresponds to the electric flux relation:

∮E⃗⋅dA=Qε0\oint \vec{E} \cdot dA = \frac{Q}{\varepsilon_0}

So, A - I.

Faraday’s Law corresponds to the law of electromagnetic induction:

∮E⃗⋅dl⃗=−dΦdt\oint \vec{E} \cdot d\vec{l} = -\frac{d\Phi}{dt}

So, B - IV.

Lenz’s Law states that the induced emf opposes the change producing it. So, C - III.

Ampere’s Law is:

∮B⃗⋅dl⃗=μ0I\oint \vec{B} \cdot d\vec{l} = \mu_0 I

So, D - II.

Therefore, the correct matching is A - I, B - IV, C - III, D - II. Hence, the correct option is A.

Common mistakes

  • Confusing Faraday’s Law with Lenz’s Law. Faraday’s Law gives the mathematical relation for induced emf, while Lenz’s Law gives the direction or opposition principle. Match Faraday’s Law with the equation and Lenz’s Law with the statement about opposing change.

  • Mixing up Gauss’s Law and Ampere’s Law because both are written as closed integrals. Gauss’s Law involves electric flux with E⃗\vec{E} over an area, whereas Ampere’s Law involves magnetic field B⃗\vec{B} around a line integral. Check whether the integral is over dAdA or dl⃗d\vec{l}.

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