JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Electromagnetic Induction

Faraday's law of electromagnetic induction, $\oint \overrightarrow{\mathrm{E}}\cdot \overrightarrow{\mathrm{d}}=-\frac{\partial {\varphi }_{\mathrm{B}}}{\partial \mathrm{t}}$, is valid only for time-varying magnetic fields. When the magnetic flux ${\varphi }_B$ changes with time, an induced electric field is produced. For static conditions ($\frac{\partial {\varphi }_{\mathrm{B}}}{\partial \mathrm{t}}=0$), this equation reduces to $\oint \overrightarrow{\mathrm{E}}\cdot \overrightarrow{\mathrm{d}}=0$, which is a different form. The other three equations (Ampère's law, conservative nature of electrostatic field, and Gauss's law) are valid for static conditions as well.