The magnetic component of electromagnetism

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A magnetic field can exist without electricity, as demonstrated by lodestone, yet the relationship between electricity and magnetism remains complex. While electricity generates magnetism, the presence of a magnetic field does not always indicate the presence of an electric field. The frequency of electromagnetic waves can characterize both electrical and magnetic components, but additional information is required for accurate characterization in materials. In a vacuum, understanding one component of electromagnetism provides insights into the other, but this relationship is less straightforward in materials. Ultimately, magnetism and electricity are intrinsically linked, with each influencing the other.
Edward Block
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May a magnetic field exist w/o electricity? Yes, as lodestone shows us but where is the electricity? Electricity generates magnetism with it. So where is the electricity with lodestone?
 
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Also, if the wavelength of the electromagnetic standing wave yields a particular characteristic frequency(HZ), does this characterize both the electrical and the magnetic component? In other words, do we ascribe Hz to the magnetic component and use that to characterize the magnetic field created?
 
You can have magnetism without electricity, but you won't find magnetism without an electric field. They're attached at the hip.

In a vacuum knowing the properties of one or the other component of electromagnetism tells you what you need to know about the other, though you need more than the frequency to do it. In materials, not so much. (Edit: Unless you know everything you need to know about the material, I suppose.)
 
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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