JEE Main 2023 — Electromagnetic Waves Question with Solution

(A) Gauss law states that the total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity. So, $\varphi =\oint \overrightarrow{E}·\mathrm{d}\overrightarrow{s}=\frac{q}{{\in }_0}$

(B) Faraday’s law explains that the direction of the current will be opposite to the direction of flux that produced it, so $\oint \overrightarrow{E}·\mathrm{d}\overrightarrow{l}=-\frac{\mathrm{d}{\varphi }_B}{\mathrm{d}t}$

(C) Gauss's law for magnetism states that the magnetic flux B across any closed surface is zero, so $\oint \overrightarrow{B}·\mathrm{d}\overrightarrow{A}=0$

(D) Ampere’s Maxwell law is stated as 

$\oint \overrightarrow{B}·\mathrm{d}\overrightarrow{l}={\mu }_0{i}_c+{\mu }_0{\in }_0\frac{\mathrm{d}{\varphi }_E}{\mathrm{d}t}$

Where $i_c=$Conduction current and 

${\in }_0\frac{\mathrm{d}{\varphi }_E}{\mathrm{d}t}=$Displacement current

Thus, A-IV, B-I, C-II, D-III