# Ampere's law.

1. Nov 28, 2009

### Yuqing

I'm a bit confused on the exact workings of Ampere's law.

Firstly, why does the shape of the Amperian loop not matter. Is there a mathematical proof that all Amperian loops are equivalent for the purpose of this law?

Secondly, the law still holds valid in the presence of external magnetic fields (ie a current producing a field but not enclosed in the loop). Clearly the magnitude of the net field will be changed from the superposition of the two fields. How is the integral able to ignore these external magnetic fields.

2. Nov 28, 2009

### Bob S

The shape is important to the extent that you want two sides to be orthogonal to the field lines, so that only the field contribution on the other two sides are non-zero if the loop encloses currents.
The contribution from currents outside the loop cancel out when Ampere's Law integral is done properly.
Bob S

3. Nov 28, 2009

### Yuqing

Is it possible to show me some mathematical proof?

4. Nov 28, 2009

### Bob S

Consider a loop in a constant magnetic field B, with two sides of the loop orthogonal to the field and two sides parallel.

B·dl = 0 around the loop is zero because one side of the loop is parallel to the field, and the other antiparallel (the dot vector product is negative).

Bob S

Last edited: Nov 28, 2009