JEE MAIN - Physics (2023 - 13th April Morning Shift - No. 14)
Which of the following Maxwell's equation is valid for time varying conditions but not valid for static conditions :
$$\oint \overrightarrow{\mathrm{E}} \cdot \overrightarrow{d l}=0$$
$$\oint \vec{B} \cdot \overrightarrow{d l}=\mu_{0} I$$
$$\oint \vec{E} \cdot \overrightarrow{d l}=-\frac{\partial \phi_{B}}{\partial t}$$
$$\oint \vec{D} \cdot \overrightarrow{d A}=Q$$
Explanation
Maxwell's equations describe the behavior of electric and magnetic fields. There are four equations, and each has a specific role. In the given options, Option C refers to Faraday's Law of Electromagnetic Induction, which is the only equation among the options that is not valid for static conditions.
Option C: Faraday's Law of Electromagnetic Induction:
$$\oint \vec{E} \cdot \overrightarrow{d l}=-\frac{\partial \phi_{B}}{\partial t}$$
This equation states that a time-varying magnetic field (changing magnetic flux, $\phi_B$) induces an electromotive force (EMF) in a closed conducting loop, creating an electric field. In static conditions, the magnetic field doesn't change over time, and there is no induced EMF. Therefore, Faraday's Law is valid for time-varying conditions but not for static conditions.
Option C: Faraday's Law of Electromagnetic Induction:
$$\oint \vec{E} \cdot \overrightarrow{d l}=-\frac{\partial \phi_{B}}{\partial t}$$
This equation states that a time-varying magnetic field (changing magnetic flux, $\phi_B$) induces an electromotive force (EMF) in a closed conducting loop, creating an electric field. In static conditions, the magnetic field doesn't change over time, and there is no induced EMF. Therefore, Faraday's Law is valid for time-varying conditions but not for static conditions.
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