### Core Logic Let's review the fundamental Maxwell's equations: 1. **Ampere - Maxwell Law** relates the magnetic path integral to conduction current and displacement current: oint vecB cdot dvecl = mu_0 i_c + mu_0 varepsilon_0 fracdphi_Edt implies textA - IV$\oint \vec{B} \cdot d\vec{l} = \mu_0 i_c + \mu_0 \varepsilon_0 \frac{d\phi_E}{dt} \implies \text{A - IV}$ 2. **Faraday's Law of Induction** states that changing magnetic flux induces an electromotive force (EMF): oint vecE cdot dvecl = -fracdphi_Bdt implies textB - III$\oint \vec{E} \cdot d\vec{l} = -\frac{d\phi_B}{dt} \implies \text{B - III}$ 3. **Gauss's Law for Electricity** relates net electric flux to enclosed charge: oint vecE cdot dvecA = fracQvarepsilon_0 implies textC - I$\oint \vec{E} \cdot d\vec{A} = \frac{Q}{\varepsilon_0} \implies \text{C - I}$ 4. **Gauss's Law for Magnetism** states that magnetic monopoles do not exist: oint vecB cdot dvecA = 0 implies textD - II$\oint \vec{B} \cdot d\vec{A} = 0 \implies \text{D - II}$ ### Step 1: Match Evaluation The match configurations are: * A rightarrow$\rightarrow$ IV * B rightarrow$\rightarrow$ III * C rightarrow$\rightarrow$ I * D rightarrow$\rightarrow$ II This perfectly corresponds to Option (3). ### Pattern Recognition Understand the integral geometries: Path integrals (line integrals oint cdot dvecl$\oint \cdot d\vec{l}$) correspond to circulating fields (induction laws like Ampere/Faraday). Surface integrals (flux integrals oint cdot dvecA$\oint \cdot d\vec{A}$) correspond to bounded charge states (Gauss laws). ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Electromagnetic Waves Class 12 Physics: Electrostatics Class 12 Physics: Magnetism and Matter