Question

Match List - I with List - II.

List - I	List - II
A. \(\nabla \cdot \vec{D}=\rho\) B. \(\nabla \cdot \vec{B}=0\) C. \(\nabla \times \vec{E}=-\dfrac{\partial \vec{B}}{\partial t}\) D. \(\nabla \times \vec{H}=\vec{J}+\dfrac{\partial \vec{D}}{\partial t}\)	I. Faraday's law of electromagnetic induction II. Ampere-Maxwell law III. Absence of magnetic monopoles IV. Gauss's law of electricity

• A. A-IV, B-III, C-I, D-II
• B. A-IV, B-III, C-II, D-I
• C. A-III, B-IV, C-I, D-II
• D. A-III, B-IV, C-II, D-I

Hint:

Important Maxwell equations: \[ \nabla\cdot\vec{D}=\rho \Rightarrow \text{Gauss law} \] \[ \nabla\cdot\vec{B}=0 \Rightarrow \text{No magnetic monopoles} \] \[ \nabla\times\vec{E}=-\frac{\partial \vec{B}}{\partial t} \Rightarrow \text{Faraday law} \] \[ \nabla\times\vec{H}=\vec{J}+\frac{\partial \vec{D}}{\partial t} \Rightarrow \text{Ampere-Maxwell law} \]

Answer 1

The Correct Option is A

Concept: The four Maxwell equations describe electromagnetic phenomena completely. Each equation has a physical interpretation.

Step 1: Match equation A. Given: \[ \nabla\cdot\vec{D}=\rho \] This represents: \[ \text{Gauss's law of electricity} \] Hence: \[ A \rightarrow IV \]

Step 2: Match equation B. Given: \[ \nabla\cdot\vec{B}=0 \] This implies:
• No isolated magnetic charges exist.
• Magnetic monopoles do not exist. Therefore: \[ B \rightarrow III \]

Step 3: Match equation C. Given: \[ \nabla\times\vec{E}=-\frac{\partial\vec{B}}{\partial t} \] This is: \[ \text{Faraday's law of electromagnetic induction} \] Thus: \[ C \rightarrow I \]

Step 4: Match equation D. Given: \[ \nabla\times\vec{H}=\vec{J}+\frac{\partial\vec{D}}{\partial t} \] This is: \[ \text{Ampere-Maxwell law} \] Therefore: \[ D \rightarrow II \]

Step 5: Write the final matching. Hence: \[ A-IV,\ B-III,\ C-I,\ D-II \]

Step 6: Write the final answer. Thus, the correct option is: \[ \boxed{(A)\ A-IV,\ B-III,\ C-I,\ D-II} \]