Discussion
Match List I with List II and select the correct answer using codes given below :
| List I | List II |
|---|---|
| (a) Maxwell's equation based on Ampere's law | (i) \(\nabla \cdot \bar{B} = 0\) |
| (b) Maxwell's second equation based on Faraday's law | (ii) \(\nabla\times\bar{H}=\left(\bar{J}+\frac{\partial\bar{D}}{\partial t}\right)\) |
| (c) Maxwell's third equation based on Gauss' law | (iii) \(\nabla \cdot \bar{D} = \rho\) |
| (d) Maxwell's fourth equation based on non-existence of magnetic monopole | (iv) \(\nabla \times \bar{E} = \dfrac{-\partial \bar{B}}{\partial t}\) |
Answer: C
The correct matching is a-ii, b-iv, c-iii, d-i.
- Ampere's law, with Maxwell's displacement current: \(\nabla \times \bar{H} = \bar{J} + \partial\bar{D}/\partial t\) (ii).
- Faraday's law: \(\nabla \times \bar{E} = -\partial\bar{B}/\partial t\) (iv).
- Gauss' law for electric fields: \(\nabla \cdot \bar{D} = \rho\) (iii).
- No magnetic monopoles: \(\nabla \cdot \bar{B} = 0\) (i).
The curl equations describe circulation (Ampere and Faraday) and the divergence equations describe sources (charge, and the absence of magnetic charge). The near-miss code swaps the two divergence equations, giving the monopole law the charge density.
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