Re: Maxwell's Equations

"Androcles" <Headmaster@xxxxxxxxxxxxxxxxxx> wrote:
"Jonah Thomas" <jethomas5@xxxxxxxxx> wrote
"Androcles" <Headmaster@xxxxxxxxxxxxxxxxxx> wrote:
"Jonah Thomas" <jethomas5@xxxxxxxxx> wrote
"Androcles" <Headmaster@xxxxxxxxxxxxxxxxxx> wrote:
"Jonah Thomas" <jethomas5@xxxxxxxxx> wrote
Here is my problem. For some entirely theoretical exploration
I'm> >> > doing, it's become clear that things would work much
smoother if> >one> > of Maxwell's equations had a sign change.

Instead of
del x E + partial dB/dt = 0 it should be

del x E - partial dB/dt = 0

Several things would work out a lot smoother for me that way.

So I'm wondering, is there actually experimental evidence for
that> > sign?

[snip response to a typo]

Is there electronics that wouldn't work right if that sign was
changed?

Electronics never work right until you build, test and debug
them.> >> I chose 'altitude' in my example above because Concorde
(with which> >I> was directly involved) ran on analogue computers
(museum pieces> >today)> which simulated altitude with a voltage.
That voltage comes> >from the> barometer which measures air pressure.
Even today, even> >with GPS> capability, all aircraft fly at
barometric altitude rather> >than> (measured with a ruler) actual
height above sea level. It is> >more> important that all planes have
the same error than some planes> >being> "wrong" and some being
"right". We know that all planes are> >flying at> the "wrong"
altitude and it becomes important near the> >ground where it> can
start to use the radar altimeter... but> >remember, the ground is>
above sea level. A mile above it for Denver.> >Barometric altitude
is> absolute, radar altitude is relative. No two> >planes> shoud be
within 5 miles of each other at the same altitude or> >else> they
should be at least 500 feet apart in> >> altitude.

Anything like that?

If I built a device to control the altitude of a plane with a
rate> >of> change of altitude designed for passenger comfort and got
the> >sign> wrong I'd change the electronics. I wouldn't think back
to my> >student> days and worry about anything my lecturer told me
that he> >got hearsay> from Maxwell. As an engineer, I'd simply
dismiss it with> >the maxim> "Those that can, do. Those that can't,
teach." I'd learn> >from my> mistake and stop trusting lecturers who
have no experience> >of the real> world. Except it never happens, one
knows which way is> >up before the> design stage. Maxwell's equations
are cast in> >concrete, nobody can> change them except Maxwell and
he's dead. Only> >academics pay any> attention to them anyway.

That's what I thought. We could have a sign change wrong in
Maxwell's equations and for 150 years the engineers would ignore
it.>
Not really. You made a typographical error which I took as
verbatim> and John Park picked up on, but
E + dB/dt = 0
is just fine if you see it in the light it was intended.

V (a constant value) = the negative going rate of change of the
magnetic flux.
Think of it this way:
The first derivative of the sine function is the cosine function.
cos(t) = d(sin(t))/dt
http://en.wikipedia.org/wiki/Trigonometric_functions

In particular, if t = 0 then sin(t) = 0, but the rate of change of
sin(t) at zero (i.e. the slope) is 1 = cos(t).

The second derivative of sin(t) = -sin(t)
The third is -cos(t)
and the fourth is the function itself, sin(t).
Compare that with the first derivative of exp(t), which is exp(t).

What E = -dB/dt is saying in a physical sense is that a collapsing
magnetic field (or reducing magnetic flux) creates a voltage E
which> is proportional to the rate of collapse. In practice this
means that> we can interrupt the current flowing
in the primary of a transformer by opening a switch, there is
nothing> to maintain the magnetic flux in the iron core,
that collapses rapidly and a voltage is generated in the secondary
winding. That voltage is responsible for the spark in your car
engine.> It also created a spark across the old-fashioned "points"
that used to> open with a cam in the distributor, but that has since
been replaced> by an electronic switch. The spark across the points
is damaging to> them, they burn away, and is caused by the collapsing
magnetic field> acting on the primary winding of the coil. To limit
the damage a> capacitor was added across them, but now you have a
circuit which> allows the current to continue to flow in the primary
after the points> have opened and that reduces the rate of collapse.
So we have a compromise, to save the points from burning away and
still get a spark at the plugs we need more
turns in the secondary winding.

**************
As to polarity, nobody really cares. We can
connect either end of the secondary winding to the body of the car,
negative spark plugs are just as good as positive spark plugs, and
a> rising magnetic field will do the same job as a falling one but
with> opposite polarity.
**************

Yes?

So -E = dB/dt.
As to the curl, you can do as you like with it. I have no use for
it> when I can direct the voltage to where I need it, at the spark
plug> with a curly wire attached, and I can diverge it with a
distributor.> http://tinyurl.com/ydhnmkx

But then, I have no use for secants, cosecants, cotangents, or any
other ratio beyond sin and cosine. I know what they are because
they> were taught to me in school, but I've never had a use for them
in any> engineering I've done, they are merely academic clutter.
Same goes> for your sign preference.

Tangent and cotangent are a shorthand when you find yourself
dividing sine by cosine or vice versa. Secant and cosecant are
shorthand for dividing by sine or cosine. They have a geometrical
meaning that can be a nice shorthand too. You can get by without
them but it means you have to use less memory and more thinking. If
you're comfortable thinking instead of remembering then you don't
lose much avoiding them.

It's simpler than that. The hypotenuse is 1, the radius of the unit
circle. You can scale it, of course. Sine is the projection of the
hypotenuse onto the y-axis ( or i-axis as I prefer to think of it),
cosine the projection onto
the x-axis. Tangent is just a ratio, sin/cos. What use is that?

Pick a point on your circle and draw a line "tangent" to it. It will be
at right angles to your hypotenuse. Extend that line to the x-axis. You
have a right triangle with length 1 for one side, the tangent of the
angle for the second side, and the secant of the angle for the
hypotenuse. sec^2 = tan^2 + 1. Of course if you pick pi/2 or -pi/2 for
your angle then the tangent and secant will be too long.

Sometimes that triangle is worth using. You can figure it all with sine
and cosine with some extra trouble. I think they used to use tan and sec
for early artillery etc. If you use it a lot then it's easier to
remember tangent formulas than derive them fresh each time from sine and
cosine. If you don't do anything that needs them then they're useless to
you.

As someone used to programming a computer (and I've had occasion
to compute sine from the Taylor series on a machine that didn't have
a library available to it, a welding robot that was installed in
Ford's F150 plant in Norfolk VA) I simply don't need to define a
tangent from memory as tan = sin/cos because the computer is still
going to compute both sin and cos first. What is useful is
precomputing n! since that will be used in every term in the Taylor
series, whatever the value for the angle. I'd rather remember the
Taylor series than remember a definition for secant or cosecant. The
robot was still a flop, though. The arc from the welding generated too
much noise in the signal cables and the robot's position was lost to
the computer. So it worked just fine on a dry run but crashed when
welding. We could test all night long but couldn't weld until the
morning shift arrived and started the plant up, then we couldn't test.
Ces't la vie. No sale.

I found the continued fraction derivation faster and more stable, but
anything that's good enough for the application is good enough.

Noise in the signal cables is a hardware problem. I once lived in a
valley right below a string of radio stations, and my toy computer got
country-western songs mixed into its data storage. I started to figure
out a way to save each 12-byte pattern repeatedly and transform the
signal, but I noticed that some times of day the songs were louder than
the signal. I called the radio station for advice and the engineer there
gave me a cable that was shielded well enough. Problem solved.

Electrical current flowed from positive to negative in Maxwell's
day,> then along came J.J. Thompson, the negative electron was born
and> suddenly the beam current of negative electrons flowed from the
cathode to the anode in a CRT. It still flows from anode to cathode
outside the tube on its way back, which it does to complete the
circuit. Early transistor radio schematics had the negative rail
at> the top because they used germanium PNP transistors and that made
them> similar to vacuum tube schematics, but before long the silicon
NPN> transistor arrived and the schematics were (and still are) drawn
with> the positive rail at the top. See, the arrow points DOWN.


http://www.best-microcontroller-projects.com/image-files/schematic-s
ymbols-transistor.png> Current still flows from +ve to -ve, even if
the electrons move up.> It is only a convention, no "experiment" will
change it.

That's what I'm asking. You give me the answer I want.

It occurs to me that I should have done a thought experiment about
the result of asking my question on sci.physics.relativity before I
asked it.

If I actually got an answer that described an experiment that showed
the original ME was right, then I'd have an answer I could live
with. But how likely is that? It would require that someone here
know that much about ME, and bother to answer.

More likely would be some random experiment that did not show it,
but which the commenter claimed did show it. Then I ask how it shows
it, and he tells me to do my own homework, he's done more than
enough to give me the experiment.

Or someone tells me that it's a convention and doesn't really
matter, I thank him, and the peanut gallery calls us both cranks for
believing ME is wrong.

There's no way to show that ME works either way without a whole lot
of work. There's no way to show ME is compatible with experiment
without a tremendous amount of work. So the only workable outcome is
one experiment that shows my way is wrong, and if there isn't one
then it's unreasonable to suppose I might get any definitive answer.

By now you should be getting an understanding that the peanut gallery
is full of peanuts. Needless to say I'm downright rude to them. It
wasn't always like that, I used to be polite to some people but ten
years of Usenet has changed me. Now I'm downright rude to everyone.

Whatever works for you. I've been surprised at the noise-to-signal ratio
here. A whole lot of times people just do the insults without actually
putting any physics into it.

If you want to experiment, connect an audio amplifier to the swing arm
of an old hard drive. It's a got a nice magnetic field already built
in. Put some music on and watch what happens.
http://zone.ni.com/cms/images/devzone/tut/Hard%20Drive%20Basics%201.png
That arc labelled "actuator" is a damned powerful magnet.

If there's some specific experiment that requires it the way
it> >is> > then I'll have to put up with it. But is there one? If
there's> >no> > specific reason not to then I'll do it the way that's
intuitively> > obvious.

Engineers aren't concerned with experiments. Every day is an
experiment. Science is about understanding Nature, not running
experiments or writing equations. If Shapiro decides light is
delayed> as it passes the Sun and puts it down to GR's curvature
of> >spacetime> then Shapiro forgot Coriolis.

http://www.androcles01.pwp.blueyonder.co.uk/Shapiro/Crapiro.htm


.

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