Match List-$I$ with List-$II$ and choose the correct answer from the options given below:
| List-$I$ | List-$II$ |
| :--- | :--- |
| $A. \oint \vec{B} \cdot d\vec{l} = \mu_0 i_c + \mu_0 \varepsilon_0 \frac{d\phi_E}{dt}$ | $I. \text{Gauss' law for electricity}$ |
| $B. \oint \vec{E} \cdot d\vec{l} = -\frac{d\phi_B}{dt}$ | $II. \text{Gauss' law for magnetism}$ |
| $C. \oint \vec{E} \cdot d\vec{A} = \frac{Q}{\varepsilon_0}$ | $III. \text{Faraday law}$ |
| $D. \oint \vec{B} \cdot d\vec{A} = 0$ | $IV. \text{Ampere-Maxwell law}$ |

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

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Match List-$I$ with List-$II$:
List-$I$ List-$II$
$A$. Gauss's Law in Electrostatics $I$. $\oint \vec{E} \cdot d \vec{l} = -\frac{d \phi_B}{d t}$
$B$. Faraday's Law $II$. $\oint \vec{B} \cdot d \vec{A} = 0$
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$D$. Ampere-Maxwell Law $IV$. $\oint \vec{E} \cdot d \vec{s} = \frac{q}{\epsilon_0}$

Choose the correct answer from the options given below:

$A$ parallel plate capacitor of area $60\, cm^2$ and separation $3\, mm$ is charged initially to $90\, \mu C$. If the medium between the plates becomes slightly conducting and the plate loses the charge at the rate of $2.5\times10^{-8}\, C/s$,what is the magnetic field between the plates?

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