Match the following Maxwell’s equations: (The symbols used here have their usual meanings)
List-$I$List-$II$
$(a)$ Gauss’ law for electrostatics$(i)$ $\oint \vec{E} \cdot d\vec{A} = \frac{Q}{\epsilon_0}$
$(b)$ Gauss’ law for magnetism(ii) $\oint \vec{B} \cdot d\vec{l} = \mu_0 [i_c + \epsilon_0 \frac{d\phi_E}{dt}]$
$(c)$ Faraday’s law(iii) $\oint \vec{B} \cdot d\vec{A} = 0$
$(d)$ Ampere-Maxwell’s law(iv) $\oint \vec{E} \cdot d\vec{l} = -\frac{d\phi_B}{dt}$

  • A
    $a-i, b-iii, c-iv, d-ii$
  • B
    $a-ii, b-iii, c-i, d-iv$
  • C
    $a-i, b-ii, c-iii, d-iv$
  • D
    $a-ii, b-iii, c-iv, d-i$

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Match List-$I$ with List-$II$ and choose the correct answer from the options given below:
| List-$I$ | List-$II$ |
| :--- | :--- |
| $A$. Gauss's law of magnetostatics | $I$. $\oint \vec{E} \cdot d\vec{a} = \frac{1}{\epsilon_0} \int \rho dV$ |
| $B$. Faraday's law of electromagnetic induction | $II$. $\oint \vec{B} \cdot d\vec{a} = 0$ |
| $C$. Ampere's law | $III$. $\oint \vec{E} \cdot d\vec{l} = -\frac{d}{dt} \int \vec{B} \cdot d\vec{a}$ |
| $D$. Gauss's law of electrostatics | $IV$. $\oint \vec{B} \cdot d\vec{l} = \mu_0 I$ |

What contradiction is found by using Ampere's circuital law to obtain the magnetic field during the charging of a capacitor?

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