Understanding Ampere's Law: What Does the Current Enclosed Mean?

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Ampere's Law relates the magnetic field around a closed loop to the electric current passing through that loop. The "current enclosed" refers to the net current that passes through the surface bounded by the loop, considering both directions. To determine the positive direction of current, the right-hand rule is applied in conjunction with the direction of integration around the loop. Understanding this concept is crucial for applying Ampere's Law effectively in electromagnetic calculations. Mastery of these principles is essential for grasping the fundamentals of electromagnetism.
JasonBourneV
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Can anyone explain to me what Ampere's Law really is? For example, what does the current encircled really mean? Is it the total current passing through the loop in either direction?
 
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Imagine a surface bounded by the closed loop. The net current passing through that surface is what you need. The positive direction is defined using the right hand rule in the direction of integration around the loop.
 
Thread 'Motional EMF in Faraday disc, co-rotating magnet axial mean flux'

Thread 'Motional EMF in Faraday disc, co-rotating magnet axial mean flux'

So here is the motional EMF formula. Now I understand the standard Faraday paradox that an axis symmetric field source (like a speaker motor ring magnet) has a magnetic field that is frame invariant under rotation around axis of symmetry. The field is static whether you rotate the magnet or not. So far so good. What puzzles me is this , there is a term average magnetic flux or "azimuthal mean" , this term describes the average magnetic field through the area swept by the rotating Faraday...
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