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Maxwell's equations: names and which hold for time-varying fields

This type of question, asked 5 times: 25 Jan 2023, 13 Apr 2023, 29 Jan 2024, 30 Jan 2024, 23 Jan 2026 S1. All 5 questions below, oldest first.

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  1. Question 1

    25 Jan 2023

    103
    Match List I with List II
    LIST ILIST II
    A. Gauss's Law in ElectrostaticsI. ∮E→⋅dl→=−dϕBdt\oint\overrightarrow{E}\cdot d\overrightarrow{l} = -\frac{d\phi_{B}}{dt}
    B. Faraday's LawII. ∮B→⋅dA→=0\oint\overrightarrow{B}\cdot d\overrightarrow{A} = 0
    C. Gauss's Law in MagnetismIII. ∮B→⋅dl→=μ0ic+μ0ϵ0dϕEdt\oint\overrightarrow{B}\cdot d\overrightarrow{l} = \mu_{0}i_{c} + \mu_{0}\epsilon_{0}\frac{d\phi_{E}}{dt}
    D. Ampere-Maxwell LawIV. ∮E→⋅ds→=qϵ0\oint\overrightarrow{E}\cdot d\overrightarrow{s} = \frac{q}{\epsilon_{0}}
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  2. Question 2

    13 Apr 2023

    1
    Which of the following Maxwell's equations is valid for time varying conditions but not valid for static conditions:

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  3. Question 3

    29 Jan 2024

    10
    Match List I with List II
    List IList II
    A. ∮B→⋅dl→=μ0ic+μ0ε0dϕEdt\oint \overrightarrow{B}\cdot\overrightarrow{dl}=\mu_{0}i_{c}+\mu_{0}\varepsilon_{0}\frac{d\phi_{E}}{dt}I. Gauss' law for electricity
    B. ∮E→⋅dl→=−dϕBdt\oint \overrightarrow{E}\cdot\overrightarrow{dl}=-\frac{d\phi_{B}}{dt}II. Gauss' law for magnetism
    C. ∮E→⋅dA→=Qε0\oint \overrightarrow{E}\cdot\overrightarrow{dA}=\frac{Q}{\varepsilon_{0}}III. Faraday law
    D. ∮B→⋅dA→=0\oint \overrightarrow{B}\cdot\overrightarrow{dA}= 0IV. Ampere Maxwell law
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  4. Question 4

    30 Jan 2024

    109
    Match List I with List II
    List-IList-II
    A. Gauss's law of magnetostaticsI. ∮E→⋅da→=1ε0∫ρ dV\oint \overrightarrow{E}\cdot\overrightarrow{da} = \frac{1}{\varepsilon_{0}}\int \rho\, dV
    B. Faraday's law of electromagnetic inductionII. ∮B→⋅da→=0\oint \overrightarrow{B}\cdot\overrightarrow{da} = 0
    C. Ampere's lawIII. ∮E→⋅dl→=−ddt∫B→⋅da→\oint \overrightarrow{E}\cdot\overrightarrow{dl} = -\frac{d}{dt}\int \overrightarrow{B}\cdot\overrightarrow{da}
    D. Gauss's law of electrostaticsIV. ∮B→⋅dl→=μ0I\oint \overrightarrow{B}\cdot\overrightarrow{dl} = \mu_{0}I
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  5. Question 5

    23 Jan 2026 S1

    3
    Match List-I with List-II.
    List-I (Relation)List-II (Law)
    (A) ∮E→⋅dl→=−ddt∮B→⋅da→\oint \overrightarrow{E} \cdot \overrightarrow{dl} = - \frac{d}{dt}\oint \overrightarrow{B} \cdot \overrightarrow{da}(I) Ampere's circuital law
    (B) ∮B→⋅dl→=μ0(I+ϵ0dϕEdt)\oint \overrightarrow{B} \cdot \overrightarrow{dl} = \mu_{0}\left( I + \epsilon_{0}\frac{d\phi_{E}}{dt} \right)(II) Faraday's laws of electromagnetic induction
    (C) ∮E→⋅da→=1ϵ0∫ρdv\oint \overrightarrow{E} \cdot \overrightarrow{da} = \frac{1}{\epsilon_{0}}\int\rho dv(III) Ampere-Maxwell law
    (D) ∮B→⋅dl→=μ0I\oint \overrightarrow{B} \cdot \overrightarrow{dl} = \mu_{0}I(IV) Gauss's law of electrostatics
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