Purcell ch5 is no better. He in effect confirms that STR infers that there is no limit to the hi-strength of a magnetic field around a current carrying wire if u make the wire thinner & thinner. And, no limit to the lo-strength if u make the wire thicker & thicker. All wires carrying the same say one Amp.
What to call it? Einstein's Magnetism Catastrophe – might do.
Uhh, no?
Is this it? Is this the culmination? That at the end of all this... you don't understand Ohm's Law or Ampere's Law or even the meaning of uniform current density?
Changing the thickness of the wire but maintaining the same current (meaning you had to change the strength of the
E-field that created the current in order to keep it constant) won't change the magnetic field strength at some distance
r away from the surface of the conductor. Not in relativity and not in Ampere's Law either.
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magin.html#c1You'll notice that Ampere's Law makes no statement about the thickness of wires versus magnetic field strength - just how far you are FROM THE CENTER of a Gaussian loop and how much current is enclosed by the Gaussian loop that the current penetrates through. Ampere's Law and Relativity are true whether wires are there or not! They're laws of nature. Magnetic fields exist in space even when wires aren't around....
It's unfortunate that Ampere's Law is always taught in the context of current-carrying wires. I can make currents in empty space with an electron gun and exactly define the magnetic field strengths around them depending on the density of the electron stream and their velocities - BTW this is how cathode-ray tube TV works. If special relativity were wrong, the images on old TVs could never be in focus:
https://www.pbs.org/newshour/science/tv-radar-guns-and-other-technology-linked-to-einsteins-theories-of-relativityRefer to example 5.4:
https://openstax.org/books/university-physics-volume-3/pages/5-3-time-dilationAnyways, I've digressed because there are just so many ways you're wrong about everything.
In Chapter 5 and later into Chapter 6 of Purcell, they used relativity to derive an identical expression of Ampere's Law starting with Gauss' Law and Coulomb's Law because they are already Lorentz invariant (which Purcell takes pains to explain). Consistent with experiment and consistent with mathematics. The only catastrophe here is you.
Einstein's MC can be added to Einstein's TC (Twins Catastrophe)(which i see that Steinmetz ignored in his 4 lectures).
LOL calm down. He was introducing relativity to people who had never heard of it before and didn't have a strong mathematical background. And there is nothing catastrophic about the twin paradox - it ain't even a paradox, really.
I see that Steinmetz too called the MMX null, when in fact the MMX showed a 6 km/s aetherwind, corrected to 8 km/s by Munera (using the proper averages), corrected to about 380 km/s by Cahill (using the proper calibration).
Yea, cause Michelson couldn't report etherwind within his own margin of error. We've been over this.
In 1925-33 approx Miller & Morley repeated the Michelson & Morley MMX & found an aetherwind of about 240 km/s, later corrected to 400 km/s by Cahill using the proper calibration. But Steinmetz died in 1923 (either from shame re the Einsteinian Twins Catastrophe, or from anxiety re the Einsteinian Magnetic Catastrophe), hence he did not have the benefit of Miller's improved MMX.
And now you're being a tool - this isn't funny. Steinmetz had health problems his whole life and he died far too young. I wish he had lived through the quantum revolution. He might've even lived to see the invention of the transistor under different circumstances.
But I am glad to see you've completely reversed course on co-opting Steinmetz for your lunacy while just hours earlier you were tentatively hoping he might back up your crankery. Steinmetz was no crank. In fact, he was a true scientist. He lived through the Ether Dark Ages, learned about relativity, realized what a brilliant and coherent theory it is, and said this about people who cling to ether,
Thus the conception of the ether; is one of those untenable hypotheses which have been made in the attempt to explain some difficulty. The more it is studied and conclusions drawn from it, the more contradictions we get, and the more unreasonable and untenable it becomes. It has been merely conservatism or lack of courage which has kept us from openly abandoning the ether; hypothesis. The belief in an ether; is in contradiction to the relativity theory, since this theory shows that there is no absolute position nor motion, but that all positions and motions are relative and equivalent.
Charles P. Steinmetz p.16
Ya hear that? Steinmetz thinks you're a coward.
Re Einstein's Magnetism Catastrophe. Einsteinist's always invoke an infinitely long wire. Did u ever wonder why it was infinitely long? Allow me to tell u. It was infinitely long koz a finitely long wire duznt work.
You're a civil engineer (apparently I guess from what you said pages ago) so I'll forgive this particular idiocy due to lack of electrical physics/mathematics education on your part.
But Ampere's Law as conventionally written doesn't work directly with finite length wires either because there is no longer charge conservation. You have to account for the boundary conditions where discontinuity exists - this breaks the symmetry of the problem and makes the integrations harder. Not impossible - just harder:
http://www.phys.uri.edu/gerhard/PHY204/tsl216.pdfhttps://scholarworks.merrimack.edu/cgi/viewcontent.cgi?article=1016&context=phy_facpubhttps://opentextbc.ca/universityphysicsv2openstax/chapter/amperes-law/Consider using Ampère’s law to calculate the magnetic fields of a finite straight wire and of a circular loop of wire. Why is it not useful for these calculations? In these cases the integrals around the Ampèrian loop are very difficult because there is no symmetry, so this method would not be useful.
OpenText BC
This works the same way in relativity but the mathematics are, again, more complicated and mostly outside the purview of Purcell's introductory text (too hard for you, I'm sorry).
The attraction (or repulsion) tween 2 finite parallel wires can't increase with relative speed, koz STR length contraction lessens the spacings tween electrons or protons, but it can't add or subtract electrons or protons from the wire(s).
What to call this? Einstein's Catastrophe For Wires With Finite Length.
It means that finite lengths of wire can't have magnetism.
They do - you just don't know how to calculate them.
How do I know you can't? Try solving the homework problems in Purcell Chapter 5 or Chapter 6 (exercise 6.5 is particularly good as is 6.28). Go ahead - try. I won't wait.
In the meantime, I have my own homework to do (and to grade).
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