Ampere's swimming rule about magnetic field around a current carrying conductor

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When current flows along the z-axis, a magnetic field is generated in the XY plane, affecting a compass placed there. A compass positioned vertically along the z-axis will respond differently based on its ability to rotate. If the compass can align with the magnetic field in its plane of rotation, it will do so. However, if the magnetic field lines are perpendicular to the plane of rotation, the compass will not rotate. Understanding these interactions is crucial for applications involving magnetic fields and current-carrying conductors.
manjuvenamma
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We know that if current is flowing in the direction of z-axis (verical), magnetic field is formed in a plance perpendicular to that line i.e., in the XY plane. That is if you keep a compass in the XY plane it will experience a force as per the rule. But what will happen to a compass that is placed vertically i.e. along the z axis?
 
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Depends on which plane it is free to rotate in. If it can align itself along the magnetic field in that plane, it will rotate and do so. If magnetic field lines are perpendicular to that plane, it cannot align itself with them, so it won't rotate.
 
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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