JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Electrostatics

Each law is fixed by the integral that states it. The outward flux of the electric field through a closed surface equalling the enclosed charge over ${ϵ}_0$ is Gauss's law in electrostatics. The line integral of the electric field round a loop equalling minus the rate of change of magnetic flux is Faraday's law. The vanishing of the magnetic flux through any closed surface is Gauss's law in magnetism. The circulation of the magnetic field driven by the conduction current together with the displacement-current term is the Ampère--Maxwell law. So Gauss's law in electrostatics goes with $\oint \vec{E}\cdot d\vec{s}=q/{ϵ}_0$, Faraday's law with $\oint \vec{E}\cdot d\vec{l}=-d{\varphi }_B/dt$, Gauss's law in magnetism with $\oint \vec{B}\cdot d\vec{A}=0$, and the Ampère--Maxwell law with $\oint \vec{B}\cdot d\vec{l}={\mu }_0{i}_C+{\mu }_0{ϵ}_{0}d{\varphi }_E/dt$.