Can Ampere's Law Confirm Zero Magnetic Field in Non-Enclosing Loops?

AI Thread Summary
Ampere's Law states that the line integral of the magnetic field around a closed loop is proportional to the net current enclosed by that loop. In scenarios where an Amperian loop does not enclose any net current, the closed line integral of the magnetic field should indeed be zero, regardless of the loop's shape. This conclusion aligns with Maxwell's equations, which support the idea that magnetic fields are influenced by enclosed currents. The discussion emphasizes the importance of understanding the relationship between current and magnetic fields in complex configurations. Ultimately, applying these principles can help clarify the behavior of magnetic fields in non-enclosing loops.
jtabije
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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.
 
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Use Maxwell's equation (the integral form), and derive this, to convince your mind :).
 

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