1. State Ampere's circuital law in differential form for the general case of an arbitrary magnetic field. How is it derived from its integral form?
2. What is the significance of a nonzero net right-lateral differential of Hx and Hy normal to the z-direction at a point in space?
3. If a pair of E and B at a point satisfies Faraday's law in differential form, does it necessarily follow that it also satisfies Ampere's circuital law in differential form, and vice versa?