I ran into something called Faraday's Paradox. I found an explanation
that seemed to dissolve the paradox, a simple explanation. In case
someone is interested, here it is:
Faraday's paradox is demonstrated as follows: Take a cylindrical magnet,
that is magnetised in the direction of its axis of symmetry. Spin the
magnet. When you measure its magnetic field, it will seem that the
magnetic field does not spin with the magnet. For example, it does not
cause a current in a stationary loop of conductive wire. But if you spin
the loop of wire instead you do get a current. Why don't you get a
current when the magnet spins?
Here is my answer. First, in place of a magnet, use an electromagnet.
Electrons travel through wires in a helix, almost a circle. They travel
around the helix at close to lightspeed, and that creates a magnetic
field. If you were to rotate the helix at say 1000 rpm how much effect
would that have on the moving electrons that create the magnetic field?
Not much. It certainly wouldn't make the magnetic field rotate. It
affects the speed of the electrons by a trivial amount, which might be
pretty much canceled out because the fixed positive charges are moving
along the same helix at the extra speed.
Now go back to the magnet. What makes it a magnet is a whole lot of
electrons that are sort of on average traveling in similar little
circles at tremendous speed. Their sum makes a magnetic field which is
exactly the same as the electromagnet. If we were to rotate the magnet
at 1000 rpm how much effect would that have on the motion of any one
electron? Of the electrons as a whole? Without doing any math I'm going
to assert that the movement of the electrons in the magnet adds up to
pretty much the same thing as the motion in the electromagnet, and so
rotating the magnet will have essentially no effect.
A magnet looks like a solid thing. Like a potato. It's only natural to
suppose that if you rotate the solid thing its magnetic field will
rotate with it, just like a potatoe's eyes will rotate with the potato.
But the magnetic field is not part of the solid magnet the way the
potatoe's eyes are part of the potato. That field depends on electrons
that already revolve in little circles about as fast as they can go, and
you'd have to rotate that magnet pretty fast to make much of a
difference. And that difference might be to just make the field a bit
stronger, not to put any continuing motion on it once the new speed of
rotation was established.
Is my explanation reasonable, or does it have a fundamental flaw that
makes it more misleading than helpful?
> I was doing remedial physics study by first picking a project and then
> finding out what physics I needed to learn to do it.
>
> I ran into something called Faraday's Paradox. I found an explanation
> that seemed to dissolve the paradox, a simple explanation. In case
> someone is interested, here it is:
>
> Faraday's paradox is demonstrated as follows: Take a cylindrical magnet,
> that is magnetised in the direction of its axis of symmetry. Spin the
> magnet. When you measure its magnetic field, it will seem that the
> magnetic field does not spin with the magnet. For example, it does not
> cause a current in a stationary loop of conductive wire. But if you spin
> the loop of wire instead you do get a current. Why don't you get a
> current when the magnet spins?
>
> Here is my answer. First, in place of a magnet, use an electromagnet.
> Electrons travel through wires in a helix, almost a circle. They travel
> around the helix at close to lightspeed
[WRONG AND IRRELEVANT! But if you do want to keep score that way, they
travel at extremely low speed compared to light, presuming that the
charge carriers really are electrons]
There certainly are flaws in your argument. I do agree that there is no
paradox. To be rigorous, you have to start with physical laws--Maxwell's
equations for example. There and similar expressions of the physics
contain current but electrons did not exist when they were formulated.
Bill
--
An old man would be better off never having been born.
If you use a conductive magnet you get a current (on the magnet periphery)
when the magnet spin.
The current is always when a lope spin. In the magnetic field the current is
stronger.
Salmon wrote: "To be rigorous, you have to start with physical
laws--Maxwell's
equations for example. There and similar expressions of the physics
contain current but electrons did not exist when they were formulated."
The Maxwell's current was like the incompressible massless fluid.
Todays current is like electron gas. Is compressible and has mass.
So if you rotate the metal disc (or a cylinder) the massive and movable
electrons migrate to the periphery. The voltage appears.
Why in the magnetic field the current is stronger I do not know now.
S*
> > Here is my answer. First, in place of a magnet, use an
> > electromagnet. Electrons travel through wires in a helix, almost a
> > circle. They travel around the helix at close to lightspeed
>
> [WRONG AND IRRELEVANT! But if you do want to keep score that way, they
> travel at extremely low speed compared to light, presuming that the
> charge carriers really are electrons]
I think if I'd said it the other way round somebody would have said I
was wrong that way too. When I tried to look this stuff up the wikipedia
articles etc were pretty unclear, though not as bad as they were about
Faraday's paradox. Some of them gave calculations to predict the speed
of electrons. The calculations depended on voltage plus a lot of
constants that depended on the volume of the copper etc. But I would
expect that at the beginning electrons would be impeded by the magnetic
field of all the charges that aren't moving. (They are moving relative
to the moving charges.) Later, as more charges move and as they move
faster, they create a magnetic field that aids their movement. This is
why there is hysteresis. None of that is mentioned in the accounts I saw
that estimated speed, only voltage. And various sources said that
signals (votage change) move very fast while electrons do not. But I'd
expect that on a voltage change the electrons would change speed slowly
at first and then more quickly.
Thank you for pointing me to this, it's another soft spot.
The trouble I have with using Maxwell's Equations is that I have to find
out the correct way to use them by seeing what will match them up with
reality first. I can't use them to predict because I won't know which
way to use them is right and which is wrong until I already know the
correct answer.
> The trouble I have with using Maxwell's Equations is that I have to find
> out the correct way to use them by seeing what will match them up with
> reality first. I can't use them to predict because I won't know which
> way to use them is right and which is wrong until I already know the
> correct answer.
If you do not know how to use Maxwell's equations correctly, how do we
know that you can use other physical laws correctly? Although most books
on E& M start out with laws like Coulomb:s law and Ampere's law to
derive Maxwell's equations, other start with Maxwell's equations as the
fundamental laws and derive the earlier laws. Julius Stratton's book is
an outstanding example.
You don't need to create new theories to explain what is happening,
nor should you until you understand the fundamentals.
I'll give you a clue: Although there is no relative motion between the
magnet and the disc it's attached to, there is still relative motion
between the connecting wires to the galvanometer and the magnet :-)
Larry
It didn't look like a new theory to me, just a commonsense look at how
to apply existing theory.
> I'll give you a clue: Although there is no relative motion between the
> magnet and the disc it's attached to, there is still relative motion
> between the connecting wires to the galvanometer and the magnet :-)
Have you tried letting the galvanometer and its connecting wires rotate
with the rest? What result did you get?
Coulomb and Ampere are quite different from EM. EM starts from Biot-Savart's
"experimental" law (magnetic whirl around a wire).
>other start with Maxwell's equations as the
> fundamental laws and derive the earlier laws. Julius Stratton's book is
> an outstanding example.
In physycs are the two approach:
1. Newtonian electrodynamics (or charge method or coulombian method) where
the forces are considered.
2. Field method where the E and B replace the forces.
Jonach prefer the Newtonian electrodynamics but he do not know (probably)
that such exists.
And what about you?
S*
When you attach to the open DC circuit an additional long wire, the signals
(votage change) move very fast. It is like the one impulse wave. Next into
the wire must flow the additional electrons. It is not easy to determine the
speed of them.
In an open DC circuit electrons flows from higher voltage to the lover. The
speed is electron density dependent.
The movement of the wire can affect the speed but proportionally to the
resistivity. The superconducted wire do not affect. Cupper only a little.
In this case you should try the Ampere Electrodynamics. The currents repel
or attract. There no magnetic whirl.
The magnet is like solenoid. The rotating disc also. So electrons are
attracted or repeled to solenoid. In the both cases the excess of electrons
appears at one side of the disc. Such excess must colect at the periphery of
the disc (the voltage appears) - like on the sphere.
Current do not affects an electron at rest. So the rotating solenoid (or
magnet) can not produce the voltage in a statinary disc.
EM is a hydraulic analogy. It is useless for the electron gas.
S*
You don't get anything, as expected.
> - Show quoted text -
The Lorentz force is a simplified form of forces. Such was enough for XX
century.
In XXI century we must use the full form. The reason:
"The book has two important messages: First, although the Lorentz force
equations and Maxwell's equations provide excellent insight into
electrodynamics, there are many cases where the abandoned Ampere equations
are superior. Second, there are still many experimental anomalies that are
not explained by any of the current scientific models and these anomalies
deserve the attention of the scientific community." From:
http://www.padrak.com/ine/NEWELBOOK.html
More details here: http://www.df.lth.se/~snorkelf/Longitudinal/node4.html
S*
> Regards,
> Vince
>
>
> This intrigues me.
> If there is no relative motion betwen the disk and B how can there be a
> lorentz force on the charges?
> It would appear that a charge moving through B experiences the lorentz force
> regardless of it's relative motion through that field?
> If the lorentz force is as I've understood it previously the charges should
> undergo separation regardless of the observer. But, this appears to be
> entirely incorrect.
> I cannot get my head around it, but that's not unusual .
> Regards,
> Vince
This was explained by Maxwll's equations before anyone knew anything
about electrons!
Your primary error is that there is no rotation of the magnetic field as
its source rotates. How can you tell that a uniform field rotates? The
trick is that the field is constant. The induced emf is a way of telling
that the disk is rotating when IT IS IN a magnetic field.
Best understanding had to wait until the special theory of relativity
was developed. The electric field and the magnetic field are not
separate fields. They are part of a single tensor field. The components
of this field consists of three electric components and three magnetic
components that form the elements of a matrix representing the tensor.
Motion of the measuring equipment affects the measured components of the
tensor so that the motion modifies these components.
Kind of, except they didn't understand how to apply Maxwell's equations
to get that result until later, right? ME predicted the speed of light
and some other things, but for most things you have to get the result
first and then you can see how ME predicts it.
> Your primary error is that there is no rotation of the magnetic field
> as its source rotates. How can you tell that a uniform field rotates?
> The trick is that the field is constant. The induced emf is a way of
> telling that the disk is rotating when IT IS IN a magnetic field.
When a wire cuts across magnetic lines of force you get a current in the
wire. When a wire rotates through the lines of force you get a current,
right? But when the magnet rotates so that the relative motion between
the magnet and the wire is the same, you don't get a current. We can
explain that by assuming that the lines of force do not rotate when the
magnet rotates.
How can you tell that a uniform field rotates? If we got a current in
the wire when the magnet rotated, that would be one way to tell. But it
doesn't happen.
So the question is how we can reconcile that reality with any kind of
reasonable model. I provided a way to do that. You say not to bother
reconciling it with a reasonable model, just derive it from ME.
> Best understanding had to wait until the special theory of relativity
> was developed. The electric field and the magnetic field are not
> separate fields. They are part of a single tensor field. The
> components of this field consists of three electric components and
> three magnetic components that form the elements of a matrix
> representing the tensor. Motion of the measuring equipment affects the
> measured components of the tensor so that the motion modifies these
> components.
That's the ticket. People who understand tensor theory well enough will
surely find that Faraday's Paradox becomes completely intuitive.
Maxwell made the proper drawings (page 38):
http://www.vacuum-physics.com/Maxwell/maxwell_oplf.pdf
See also pages: 5, 17, 18, 20, 34, 35 and 37.
>They are part of a single tensor field. The components
> of this field consists of three electric components and three magnetic
> components that form the elements of a matrix representing the tensor.
> Motion of the measuring equipment affects the measured components of the
> tensor so that the motion modifies these components.
Math is to calculate something. To description Maxwell use English. Try the
same.
S*
.
> When a wire cuts across magnetic lines of force you get a current in the
> wire. When a wire rotates through the lines of force you get a current,
> right? But when the magnet rotates so that the relative motion between
> the magnet and the wire is the same, you don't get a current. We can
> explain that by assuming that the lines of force do not rotate when the
> magnet rotates.
>
> How can you tell that a uniform field rotates? If we got a current in
> the wire when the magnet rotated, that would be one way to tell. But it
> doesn't happen.
The fallacy arises from the assumption that there is significance to the
lines of force. Lines of force have never been shown to exist. Only
magnetic fields exist, not lines of force. The pattern of iron filings
attached to a rotating magnet shows the direction of the magnetic
field. It does not show lines of force. Consequently, when you try to
use lines of force in explanations, it is not surprising that you get
incorrect conclusions. In the integral form of the law of induction, you
are measuring the motion of a boundary THROUGH a magnetic field.
> Math is to calculate something. To description Maxwell use English. Try the
> same.
You have a serious misapprehension. While mathematics can be used for
calculation by being reduced to arithmetic, the purpose of the
mathematics is to provide UNDERSTANDING.
Brilliant as Faraday was, I doubt that he would be able to describe what
Maxwell developed mathematically by mere words.
There isn't a Lorentz force on the charges in the disc, but there is
on the charges within the connecting wires to the disc and the
galvanometer/load/voltmeter etc because there is relative motion
between the B field and the electrons there. Time and time again,
people have cooked up weird and wackey theories to explain how non
relative motion between the disc and the B field gives rise to a
Lorentz force, without looking at the whole circuit.
Short the (+) and (-) leads of a voltmeter together, creating a large
loop area, and waggle a magnet near them:- You'll get a flickering
reading. Now put the magnet and voltmeter with the shorted leads on a
moveable surface, and violently shake it while keep their relative
position of the voltmeter and magnet constant. Do you get a flickering
reading? Nope.
> It would appear that a charge moving through B experiences the lorentz force
> regardless of it's relative motion through that field?
The Lorentz force depends only on relative motion between B and the
charge.
> If the lorentz force is as I've understood it previously the charges should
> undergo separation regardless of the observer.
Correct.
>But, this appears to be
> entirely incorrect.
> I cannot get my head around it, but that's not unusual .
> Regards,
> Vince
Are things clearer now?
Correct.
Are things clearer now?
Yes, thank you.
That might be a good way to explain it.
You get observable effects when charges move through variations in
magnetic field strength. No actual change, no effect.
No, that isn't it, because you get the result when the loop rotates,
just not when the magnet rotates. There's something else going on.
Also, when the loop and magnet rotate together.
Maxwell did it. See the page 5:
http://www.vacuum-physics.com/Maxwell/maxwell_oplf.pdf
Faraday said that in space are flows or stresess.
Maxwell choose flows and describe they matematically. May be that somebody
else described the stresess. Do you know?
But nobody is able to describe the todays "Maxwell's equations". They were
written by Heaviside and modified by many.
Each theory must be in agreement with the experiments. The XX century
experiments showed that the electricity is compressible (at straight and
rotational movements) and that the radio waves are like the sound waves.
Faraday and Maxwell did not know that.
S*
> > Electrons travel through wires in a helix, almost a circle. They
> > travel around the helix at close to lightspeed
>
> [WRONG AND IRRELEVANT! But if you do want to keep score that way, they
> travel at extremely low speed compared to light, presuming that the
> charge carriers really are electrons]
After some study, I believe that your approach is not useful.
If you look at all the electrons that could possibly move, and you
divide the net change in position by that number of electrons, you will
find that the average motion is quite slow. There are probably some
circumstances when it's useful to pay attention to that.
But the actual situation is that the electrons are moving very fast, but
for fairly short distances before they change direction. And if you
cancel out the movement that cancels out, what you have left over is a
few electrons traveling very fast in the direction of the current. (Or
rather in the opposite direction, since people decided on the convention
for current flow before they found out about electrons and they
accidentally decided to think of it as the other direction.)
So when I'm interested in the effect that motion of a current-carrying
wire has on the electrons that are moving, knowing that everything else
cancels out, it's a few electrons that are traveling very fast at that
time. The average speed, on the assumption that any electron is likely
to move sometime, is not useful for this. What we care about is the
electrons that are actually moving that don't average out.
However, I think you are probably right that it's irrelevant. Because
once the current reaches its steady state, there will be as many
stationary positive charges as there are moving electrons, and when you
move the wire you move both protons and electrons. So unless there are
nonlinear effects of some kind, those two will cancel out. When you give
two opposite charges the exact same additional velocity....
Are there nonlinear effects I've missed? When one charge is traveling at
near lightspeed and the other is not, would that make a nonlinearity
that would keep them from canceling?
> When a wire cuts across magnetic lines of force you get a current in the
> wire. When a wire rotates through the lines of force you get a current,
> right? But when the magnet rotates so that the relative motion between
> the magnet and the wire is the same, you don't get a current. We can
> explain that by assuming that the lines of force do not rotate when the
> magnet rotates.
>
> How can you tell that a uniform field rotates? If we got a current in
> the wire when the magnet rotated, that would be one way to tell. But it
> doesn't happen.
The problem Jonah, is that nobody knows if a magnetic field rotates
with the magnet or not! The argument has been going on (and
continues) since the days of Faraday. It has been shown that if you
try to use a coil of wire to show this, then you get correct answers
with EITHER assumption (but with different explanations). There are
ways to resolve the issue, which are complicated but not anything as
complex as say particle physics, but as far as I know nobody has done
the experiment or at least published the results. But as far as is
known electrons do travel at the high velocities in a wire, but in
random motion. The average velocity in the direction of the current
(known as "drift velocity" is very low. You could walk faster.
> So the question is how we can reconcile that reality with any kind of
> reasonable model. I provided a way to do that. You say not to bother
> reconciling it with a reasonable model, just derive it from ME.
to reply to your proposed "explanation", allow me to quote H.L.
Menchen: "There is always an easy solution to every human problem.
Neat, plausible, and wrong."
That might likely be interesting. It probably wouldn't take a whole lot
of money to set up, right?
> But as far as is
> known electrons do travel at the high velocities in a wire, but in
> random motion. The average velocity in the direction of the current
> (known as "drift velocity" is very low. You could walk faster.
Yes. But after the random motion cancels out, the nonrandom motion at
any one time consists of a few electrons traveling very fast. The drift
velocity is what you get when you average the random motion together
with the nonrandom motion. I'm sure there are circumstances where that
average value is useful.
Like, if you have a battlefield and it turns out that 1,000,000 bullets
get shot westward, while 1,001,000 bullets get shot eastward, it would
be possible to average those results and say that the net effect is that
about 2,000,000 bullets have drifted to the east at 1 foot/second. But a
soldier on the battlefield might not think that statistic was useful to
him.
> > So the question is how we can reconcile that reality with any kind
> > of reasonable model. I provided a way to do that. You say not to
> > bother reconciling it with a reasonable model, just derive it from
> > ME.
>
> to reply to your proposed "explanation", allow me to quote H.L.
> Menchen: "There is always an easy solution to every human problem.
> Neat, plausible, and wrong."
Sure, but you have given no reason whatsoever to think that my
explanation is wrong.