Match List I with List II, Gauss's Law of Magnetostatics, Faraday's law of electromagnetic induction

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Q.
Match List I with List II

List I List II

A Gauss's Law of Magnetostatics I $\oint \vec{E} \cdot \vec{d} a = \frac{1}{ϵ_{0}} \int ρ d V$

B Faraday's law of electromagnetic induction II $\oint \vec{B} \cdot \vec{d} a = 0$

C Ampere's Law III $\oint \vec{E} \cdot \vec{d} l = \frac{d}{d t} \int \vec{B} \cdot \vec{d} a$

D Gauss's law of Electrostatics IV $\oint \vec{B} \cdot \vec{d} l = μ_{0} I$

Choose the correct answer from the options given below: [2024]

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

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

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

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

Ans.
(4)

(A) Gauss of magnetostatics $\to \oint \vec{B} \cdot d \vec{a} = 0$ (II)

  (B) Faraday's law $\to \int \vec{E} \cdot d \vec{t} = - \frac{d}{d t} \int \vec{B} \cdot d \vec{a}$ (III)

  (C) Ampere's law $\to \oint \vec{B} \cdot \vec{d t} = μ_{0} I$ (IV)

  (D) Gauss of electro $\to \oint \vec{E} \cdot d \vec{a} = \frac{1}{ϵ_{0}} \int ρ d V$ (I)

Solution

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

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

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

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

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	List I		List II
A	Gauss's Law of Magnetostatics	I	$\oint \vec{E} \cdot \vec{d} a = \frac{1}{ϵ_{0}} \int ρ d V$
B	Faraday's law of electromagnetic induction	II	$\oint \vec{B} \cdot \vec{d} a = 0$
C	Ampere's Law	III	$\oint \vec{E} \cdot \vec{d} l = \frac{d}{d t} \int \vec{B} \cdot \vec{d} a$
D	Gauss's law of Electrostatics	IV	$\oint \vec{B} \cdot \vec{d} l = μ_{0} I$

Solution

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

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

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

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

Ans. (4) (A) Gauss of magnetostatics →∮B→⋅da→=0 (II) (B) Faraday's law →∫E→⋅dt→=-ddt∫B→⋅da→ (III) (C) Ampere's law →∮B→⋅dt→=μ0I (IV) (D) Gauss of electro →∮E→⋅da→=1ϵ0∫ρdV (I)

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