"Changing electric field produces magnetic field". Explain the importance of the given statement.

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(N/A) Maxwell logically demonstrated that a changing electric field induces a magnetic field. This phenomenon is of fundamental importance in physics.
Historically, the connection between electricity and magnetism was first observed by Oersted, who showed that a current-carrying wire produces a magnetic field.
This phenomenon is crucial for explaining the existence and propagation of electromagnetic waves, including radio waves, gamma rays, and visible light.
Specifically, the production of a magnetic field by a changing electric field is mathematically described by the displacement current term added to Ampere's circuital law, which is essential for understanding the charging of a capacitor.

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

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