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Classic Electromagnetism 
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#19
Nov203, 12:26 PM

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(2) The relativistic charge density is the rest charge density multiplied by the γ factor (if I remember correctly). (3) I agree with this, but it is apparently still quite popular to speak of the mass as a component of a tensor (the timelike component of the fourmomentum). It is almost the same thing with charge, but charge density really. The charge density is the timelike component of the electric fourcurrent. By charge density, I mean, that part of the electric fourcurrent that effects the electric field components of the Farady tensor, as opposed to the magnetic field components. 


#20
Nov203, 04:20 PM

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Is this how you understand it? 


#21
Nov203, 04:42 PM

P: 837

When you accelerate a charge, the changing electric field generates a changing magnetic field, which in turn generates a changing electric field, etc., to produce an electromagnetic wave.
However, it is a mistake to claim that all of magnetic fields are produced from changing electric fields, or are related to waves, or something like that. Consider electrostatics and magnetostatics. And no, the "radiant lines" in the linked site's figures do not represent both electric and magnetic fields. It was a diagram of just the electric field. The magnetic field of a moving point charge isn't radial at all. For that matter, a charge at rest doesn't radiate a magnetic field at all (unless you're including an intrinsic magnetic moment due to its spin, which I'm not; I'm just considering a classical point charge). 


#22
Nov203, 04:58 PM

P: 5,625

The word "kinks" used at the site is acceptable. supports your point, and I've never heard of magnetostatics so you'll have to fill me in to the extent it's necessary to understand how it supports your point. 


#23
Nov203, 05:06 PM

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#24
Nov203, 05:29 PM

P: 5,625

The magnetic fields, in these situations, are in fact "kinks" in the electric field. 


#25
Nov203, 06:09 PM

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What did you think the definition of "electrostatics" was? 


#26
Nov203, 08:15 PM

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#27
Nov203, 08:45 PM

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#28
Nov303, 07:47 AM

P: 5,625

The field as a whole can be regarded as "static" only in the sence there is no change in its intensity or polarity, but the field itself arises from the constant changes in the positions of the electrons whose electric fields are the basis of the magnetic field. The change in position is an acceleration in this case, and since we are already agreed on kinks arising in cases of acceleration of charges, I hope we can agree on kinks in this case of acceleration of charges. 


#29
Nov303, 09:58 AM

P: 837

In a wire, the electrons do move in straight line uniform motion. In a permanent magnet, electrons can sort of be thought of as classically moving around in circles. (Although this is not the whole reason why atoms in a magnet can have a magnetic moment; there is also the intrinsic magnetic moment.) Classically, this system would radiate electromagnetic waves, so changes in the field would propagate outward as "kinks" at the speed of light, carrying energy away from the system. However, quantum mechanically, this radiation does not happen  the fields are static, nothing propagates away. (That's why atoms don't collapse.) 


#30
Nov403, 08:33 AM

P: 27

Zooby:
Did you catch that it is acceleration relative to an EMF that produces an electromagnetic wave, not Newtonian spacial acceleration? A constant current in a coil (with a circular EMF), although changing position relative to Newtonian space, does not radiate energy. But a constant current there, or anywhere, maintains a constant field there including a (claimed) circular component around the current called: magnetic. 


#33
Nov403, 12:23 PM

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#34
Nov403, 01:04 PM

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If you meant "the AmpereMaxwell equation" as the tensor equation, then I guess I do agree. But I interpretted you to mean one of the four Maxwell equations. 


#35
Nov403, 01:15 PM

P: 837

In any case, the F itself contains no information about how changes in anything influence anything else; that's what the field equation (Maxwell's equations) is for. Whether you write Maxwell's equations in pretty covariant tensor form, or use differential forms, or geometric algebra, or quaternions, or coordinates, doesn't matter: you're still using Maxwell's equations, and the Maxwell equation that describes how a changing E field affects a B field is the AmpereMaxwell law, regardless of whether or not you consider it to be unified with other of Maxwell's equations. 


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