Curious about Ampere's Law

jtabije

I had a thought that I hope you could give me feedback on:

Imagine a complex configuration that had a steady current, such that it's magnetic field was complex as well (I apologize for using 'complex' quite loosely here). If I were to apply Ampere's Law and form an Amperian loop that did not enclose any net current, would that imply that the closed line integral of the magnetic field along the loop is zero (regardless of the Amperian loop's shape)?

My brain is saying it's zero, but my mind is not yet convinced. Hopefully you can provide me a little more insight.

With thanks,
J.

mfb

Use Maxwell's equation (the integral form), and derive this, to convince your mind :).