Discussion
Match the following lists :
| List - I | List - II |
|---|---|
| a. \(\nabla \times \overline{E}\) | i. Zero |
| b. \(\nabla \times \overline{H}\) | ii. \(\rho\) |
| c. \(\nabla \cdot (\nabla \times \overline{E})\) | iii. \(\overline{J} + \frac{\partial \overline{D}}{\partial t}\) |
| d. \(\nabla \cdot \overline{D}\) | iv. \(-\frac{\partial \overline{B}}{\partial t}\) |
Answer: C
The correct match is \(\nabla \times \overline{E}\) with \(-\partial \overline{B}/\partial t\) (iv), \(\nabla \times \overline{H}\) with \(\overline{J} + \partial \overline{D}/\partial t\) (iii), \(\nabla \cdot (\nabla \times \overline{E})\) with zero (i) and \(\nabla \cdot \overline{D}\) with \(\rho\) (ii), so the code is iv iii i ii, option (C).
These are Faraday's law, Ampere's law with displacement current, the identity that the divergence of a curl is zero, and Gauss's law. Options A, B and D exchange some of these, for example giving the charge density to the curl of H.
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