# The Relation between the integral and differential form of Amperes Law

1. Mar 30, 2013

### 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

2. Mar 30, 2013

### Staff: Mentor

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.

3. Mar 30, 2013

### Zook104

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

4. Mar 30, 2013

### Staff: Mentor

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