Maxwell's Equations Matching

The question requires matching each of Maxwell's equations (List - I) with its corresponding physical law or principle (List - II).

Analysis of Equations and Laws

• A. $\nabla \cdot \vec{D} = \rho$: This equation represents Gauss's law for electricity. It relates the divergence of the electric displacement field ($\vec{D}$) to the volume charge density ($\rho$). This matches with IV. Gauss's law of electricity.
• B. $\nabla \cdot \vec{B} = 0$: This equation represents Gauss's law for magnetism. It states that the divergence of the magnetic field ($\vec{B}$) is always zero, which implies the absence of magnetic monopoles. This matches with III. Absence of magnetic monopoles.
• C. $\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}$: This equation is Faraday's law of electromagnetic induction. It relates the curl of the electric field ($\vec{E}$) to the negative time rate of change of the magnetic field ($\vec{B}$). This matches with I. Faraday's law of electromagnetic induction.
• D. $\nabla \times \vec{H} = \vec{J} + \frac{\partial \vec{D}}{\partial t}$: This equation is the Ampere-Maxwell law. It relates the curl of the magnetic field intensity ($\vec{H}$) to the current density ($\vec{J}$) and the time rate of change of the electric displacement field ($\vec{D}$). This matches with II. Ampere-Maxwell law.

Correct Matching

Based on the analysis:

• A matches with IV
• B matches with III
• C matches with I
• D matches with II

Therefore, the correct combination is A-IV, B-III, C-I, D-II.

Final Answer

The correct option is the one that lists the matching as A-IV, B-III, C-I, D-II.

Option 1: A-IV, B-III, C-I, D-II