General > General Technical Chat

Veritasium -- How Special Relativity Makes Magnets Work.

(1/47) > >>

aetherist:
On the other Veritasium thread/topic/subject we got sidetracked a little.  https://www.eevblog.com/forum/chat/veritasium-(yt)-the-big-misconception-about-electricity/msg4077409/#msg4077409
We mentioned the Faraday Disc Paradox (re the spin or non-spin of a magnetic field)(i will link later).
We mentioned the Purcell book (re the relativistic cause of magnetism near a wire carrying an electric current)(i will link later).
Purcell refers to the (Henry) Rowland-X (re a charged spinning disc). The first supposed proof that drifting electrons in a wire can make a magnetic field (i will link later). 

I had a look at the youtube by (Derek) Veritasium (link below). And 2 youtubes by (Nick) The Science Asylum (i will show links later).
All of these Einsteinian STR explanations for the relativistic cause of magnetism near a wire carrying an electric current are krapp. I will show links & i will point out errors later.

How Special Relativity Makes Magnets Work
3,122,546 views     Sep 23, 2013     Veritasium       11.6M subscribers    .  6,631 Comments   

Magnetism seems like a pretty magical phenomenon. Rocks that attract or repel each other at a distance - that's really cool - and electric current in a wire interacts in the same way. What's even more amazing is how it works. We normally think of special relativity as having little bearing on our lives because everything happens at such low speeds that relativistic effects are negligible. But when you consider the large number of charges in a wire and the strength of the electric interaction, you can see that electromagnets function thanks to the special relativistic effect of length contraction. In a frame of reference moving with the charges, there is an electric field that creates a force on the charges. But in the lab frame, there is no electric field so it must be a magnetic field creating the force. Hence we see that a magnetic field is what an electric field becomes when an electrically charged object starts moving.

aetherist:
Here are the 2 youtubes by Nick at The Science Asylum.  I will comment later.

How Special Relativity Fixed Electromagnetism 307,828 views  Sep 12, 2019  The Science Asylum             530K subscribers       
Electrodynamics (electricity and magnetism) is governed by Maxwell's equations and the Lorentz force law, but that left it a little broken. It would take Albert Einstein inventing special relativity to fix it. If magnets are based on motion and motion is relative, how does that work?


Magnetic Force Does NOT Exist!   354,172 views       Apr 4, 2016      The Science Asylum   531K subscribers
We've all played with magnets before watching them attract or repel via magnetic force. In this video, I make the bold claim that magnetic force doesn't actually exist. It's an illusion.

aetherist:
There are many youtubes re the Faraday Disc Paradox, these 2 might be the best (by Doug Marett i think).
Purcell in his book says that there is a relativistic explanation. I will link & comment on that later.

Faraday paradox unipolar dynamo demo Part1   38,653 views  Aug 27, 2014     plenum88       1.57K subscribers   
This video is a demonstration of the Faraday paradox using a 3D printed unipolar dynamo The unipolar generator is composed of three key elements - a copper disk, a ring magnet, and a stator wire circuit to the oscilloscope, all three of which are independently rotatable. A stepper motor is used to set rotation at a fixed speed, using an Arduino control board. In part 1, we explore the essential elements of the paradox, namely the apparent magnetic induction which occurs between the co-rotating disk and magnetic elements in the device. The controversy reduces to the key question: do the magnetic lines of force rotate with the magnet or not? Einstein and Maxwell / Faraday disagreed on this point, which has also been phrased: what is the seat of the electromagnetic induction? To be continued with part2.



Faraday Paradox Unipolar Dynamo Part 2: The Solution 15,845 views  Oct 31, 2016   plenum88           1.57K subscribers    95 Comments 
In this part 2 of our Faraday Paradox series, we explore the explanations of the effect and examine some scientific papers and patents that would appear to explain the paradox. 

aetherist:
Here is the link to Purcell's book, plus some snippets. Purcell says that STR explains magnetism. Nope, he is wrong. I will comment later.

https://cdn.bc-pf.org/resources/physics/Theory/Purcell-electricity_and_magnetism_3rd_edition.pdf
5.9 Interaction between a moving charge and other moving charges.

Equation (5.1) tells us that there can be a velocity-dependent force on a moving charge. That force is associated with a magnetic field, the sources of which are electric currents, that is, other charges in motion. Oersted’s experiment showed that electric currents could influence magnets, but at that time the nature of a magnet was totally mysterious. Soon Ampère and others unravelled the interaction of electric currents with each other, as in the attraction observed between two parallel wires carrying current in the same direction. This led Ampère to the hypothesis that a magnetic substance contains permanently circulating electric currents. If so, Oersted’s experiment could be understood as the interaction of the galvanic current in the wire with the permanent microscopic currents that gave the compass needle its special properties. Ampère gave a complete and elegant mathematical formulation of the interaction of steady currents, and of the equivalence of magnetized matter to systems of permanent currents. His brilliant conjecture about the actual nature of magnetism in iron had to wait a century, more or less, for its ultimate confirmation.

Whether the magnetic manifestations of electric currents arose from anything more than the simple transport of charge was not clear to Ampère and his contemporaries. Would the motion of an electrostatically charged object cause effects like those produced by a continuous galvanic current? Later in the century, Maxwell’s theoretical work suggested the answer should be yes. The first direct evidence was obtained by Henry Rowland, to whose experiment we shall return at the end of Chapter 6.

From our present vantage point, the magnetic interaction of electric currents can be recognized as an inevitable corollary to Coulomb’s law. If the postulates of relativity are valid, if electric charge is invariant, and if Coulomb’s law holds, then, as we shall now show, the effects we commonly call “magnetic” are bound to occur. They will emerge as soon as we examine the electric interaction between a moving charge and other moving charges. A simple system will illustrate this.

Figure 5.22. A test charge q moving parallel to a current in a wire. (a) In the lab frame, the wire, in which the positive charges are fixed, is at rest. The current consists of electrons moving to the right with speed v0. The net charge on the wire is zero. There is no electric field outside the wire. (b) In a frame in which the test charge is at rest, the positive ions are moving to the left with speed v, and the electrons are moving to the right with speed v'0. The linear density of positive charge is greater than the linear density of negative charge. The wire appears positively charged, with an external field E'r, which causes a force qE'r on the stationary test charge q. (c) That force transformed back to the lab frame has the magnitude qE'r/γ, which is proportional to the product of the speed v of the test charge and the current in the wire, −λ0v0.

In the lab frame of Fig. 5.22(a), with spatial coordinates x, y, z, there is a line of positive charges, at rest and extending to infinity in both directions. We shall call them ions for short. Indeed, they might represent the copper ions that constitute the solid substance of a copper wire. There is also a line of negative charges that we shall call electrons. These are all moving to the right with speed v0. In a real wire the electrons would be intermingled with the ions; we’ve separated them in the diagram for clarity. The linear density of positive charge is λ0. It happens that the linear density of negative charge along the line of electrons is exactly equal in magnitude. That is, any given length of “wire” contains at a given instant the same number of electrons and protons. 
[9] [9 It doesn’t have to, but that equality can always be established, if we choose, by adjusting the number of electrons per unit length. In our idealized setup, we assume this has been done.]
The net charge on the wire is zero. Gauss’s law tells us there can be no flux from a cylinder that contains no charge, so the electric field must be zero everywhere outside the wire. A test charge q at rest near this wire experiences no force whatsoever.

Suppose the test charge is not at rest in the lab frame but is moving with speed v in the x direction. Transform to a frame moving with the test charge, the x', y' frame in Fig. 5.22(b). The test charge q is here at rest, but something else has changed: the wire appears to be charged! There are two reasons for that: the positive ions are closer together, and the electrons are farther apart. Because the lab frame in which the positive ions are at rest is moving with speed v, the distance between positive ions as seen in the test charge frame is contracted by1−v2/c2, or 1/γ. The linear density of positive charge in this frame is correspondingly greater; it must be γλ0. The density of negative charge takes a little longer to calculate, for the electrons were already moving with speed v0 in the lab frame. Hence their linear density in the lab frame, which was −λ0, had already been increased by a Lorentz contraction. In the electrons’ own rest frame the negative charge density must have been −λ0/γ0, where γ0 is the Lorentz factor that goes with v0.

Now we need the speed of the electrons in the test charge frame in order to calculate their density there. To find that velocity (v'0 in Fig. 5.22(b)) we must add the velocity −v to the velocity v0, remembering to use the relativistic formula for the addition of velocities (Eq. (G.7) in Appendix G).

aetherist:
Here is the link to Purcell's book, plus some of his snippets re the experiment by Henry Rowland re a charged spinning disc, the first supposed proof that drifting electrons in a wire can make a magnetic field (see link below). 
https://cdn.bc-pf.org/resources/physics/Theory/Purcell-electricity_and_magnetism_3rd_edition.pdf
https://archive.org/details/physicalpapersof00rowlrich
https://archive.org/stream/physicalpapersof00rowlrich/physicalpapersof00rowlrich_djvu.txt

6.8 Rowland’s experiment.
As we remarked in Section 5.9, it was not obvious 150 years ago that a current flowing in a wire and a moving electrically charged object are essentially alike as sources of magnetic field. The unified view of electricity and magnetism that was then emerging from Maxwell’s work suggested that any moving charge ought to cause a magnetic field, but experimental proof was hard to come by. That the motion of an electrostatically charged sheet produces a magnetic field was first demonstrated by Henry Rowland, the great American physicist renowned for his perfection of the diffraction grating. Rowland made many ingenious and accurate electrical measurements, but none that taxed his experimental virtuosity as severely as the detection and measurement of the magnetic field of a rotating charged disk. The field to be detected was something like 10−5 of the earth’s field in magnitude –a formidable experiment, even with today’s instruments!  In Fig. 6.31, you will see a sketch of Rowland’s apparatus and a reproduction of the first page of the paper in which he described his experiment. Ten years before Hertz’s discovery of electromagnetic waves,  Rowland’s result gave independent, if less dramatic, support to Maxwell’s theory of the electromagnetic field.

Navigation

[0] Message Index

[#] Next page

There was an error while thanking
Thanking...
Go to full version
Powered by SMFPacks Advanced Attachments Uploader Mod