Electromagnetic Waves Part 2

Concept:Each equation in List-I represents a fundamental law of electromagnetism.Explanation:Step 1: Relation A is $\oint \overrightarrow{E} \cdot \overrightarrow{dl} = -\frac{d}{dt} \oint \overrightarrow{B} \cdot \overrightarrow{da}$.It states that the line integral of electric field around a closed loop equals the negative rate of change of magnetic flux.This is Faraday's law of electromagnetic induction.So A matches with II.Step 2: Relation B is $\oint \overrightarrow{B} \cdot \overrightarrow{dl} = \mu_0 \left( I + \varepsilon_0 \frac{d\Phi_E}{dt} \right)$.It includes both conduction current $I$ and displacement current $\varepsilon_0 \frac{d\Phi_E}{dt}$.This is the Ampere-Maxwell law, the modified form of Ampere's circuital law.So B matches with III.Step 3: Relation C is $\oint \overrightarrow{E} \cdot \overrightarrow{da} = \frac{1}{\varepsilon_0} \int_{V} \rho \, dV$.It states that electric flux through a closed surface equals the enclosed charge divided by $\varepsilon_0$.This is Gauss's law of electrostatics.So C matches with IV.Step 4: Relation D is $\oint \overrightarrow{B} \cdot \overrightarrow{dl} = \mu_0 I$.It states that line integral of magnetic field around a closed loop equals $\mu_0$ times the enclosed current.This is the original Ampere's circuital law for steady currents.So D matches with I.Thus the correct matching is A-II, B-III, C-IV, D-I.Answer:Option B: A-II, B-III, C-IV, D-I.