The Relation between the integral and differential form of Amperes Law

[Zook104]

The integral form of Ampere's law in vacuum is

∫B$\cdot$dl=μ$_{0}$I

(a) Using the relation between I and J, obtain the differential form of Ampere's
law. You may ignore any displacement current.

(b)Define the displacement current density J$_{d}$ in terms of the displacement
field D and show how it modifies the differential form of Ampere's law.

My attempts at this have circular and achieved no useful answers. So all and any help would be greatly appreciated :D

 

[mfb]

You can consider special paths for the integration - like squares or circles - and then let their size go to zero. The interesting part is how you get rot(B) out of that limit.

 

[Zook104]

I am sorry but I don't understand what you mean?

 

[mfb]

Can you be more specific where the problem is?
Alternatively, can you show your previous attempts?