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[vox] physics time (was: Smoothing out the powerline signal?)
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[vox] physics time (was: Smoothing out the powerline signal?)



hey there,

i've been really busy lately, so i haven't been following this thread.
my favorite brand of mathematics is differential geometry.  but my *2nd*
favorite brand of math is vector calculus.  the the study of E+M IS the
study of vector calculus.  ergo, i really like E+M.  :-)

begin ME <dugan@passwall.com> 
> On Tue, 26 Mar 2002, Mark K. Kim wrote:
> > On Tue, 26 Mar 2002, ME wrote:
> > > How close is your fridge to your computer and other devices?
> > 
> > Umm... it's a mini fridge... doubly serving as my printer stand :)
> > 
> > I can't believe an EM from the fridge can disturb a huge device like an
> > electron gun inside the CRT, especially when the monitor is shielded.

i think that depends on the current draw, since the magnetic field from
a wire is, roughly:

   B = I*L / distance from wire     (see my comment on biot-savart below)

> > Plus, the power line is fluctuating all the time (60Hz) but that's not
> > very apparent at all; why would it become so apparent only when the fridge
> > turns on/off?  Can you convince me it's at least plausible?
 
when a "fridge turns on", what actually happens is that a compressor
turns on.  it compresses a gas to above atmosphere pressure, puts it in
the vicinity of the place you want to cool and then lets the gas rapidly
(adiabatically) expand.

the first law of thermodynamics says:

change in energy = change in heat energy - work done on the system

delta U          = dQ + dW
delta U          = C delta T + P delta V

C is the heat capacity (constant), P is pressure, V is volume, T is
temperature.  in the case of a fridge, the change in energy = 0 (assume
an ideal fridge).  this gives:

C delta T = -P delta V

so if you let a gas expand rapidly, delta V goes up.  this makes delta T
negative.  the gas cools.

anyway, compressors are notoriously *very* current intensive.  without
the compressor going, a fridge should draw almost no current at all.  i
think it really does pass the plausible test.

> Now, the amount of EMI generated by a powered device is (for the most
> part) rather steady. (Yes, I know it is not entirely true, but just for
> simplicity let us assume it is.)

i'm not sure that's right.  it's all based on current draw, and a fridge
draws a huge current when the compressor is on, and almost none when the
compressor is off.

> Now, in the case of a device shifting on, there is (assuming no other
> devices, and ignoring the earth's own field,

at 10^-4 tesslas, the earth's B field ain't gonna do much of anything.
:)

> It is possible to generate electron flow with magnets (magneto, or think
> turbine with hydro-electric power),

modification: it's possible to generate electron flow with magnets
*moving* relative to a conductor.  the key here is moving.  no moving
magnets, no induction.

> but it is also possible to create a
> strong magnet with electron flow. They are actually linked.

faraday's law (differential form):

the curl of E = - time derivative of B

so a changing magnetic field is a source for a non-conservative electric
field.  helmholtz theorem states that any vector field A can be written
down as a sum of a curl source and a divergence source:

A = curl(B) + div(f)

for some vector potential B and scalar potential f.  so the electric
field has a conservative divergence source (stationary charges)  and
non-conservative curl source (changing magnetic field).


faraday's law (integral form):

EMF = -time derivative of magnetic flux

magnetic flux is is "how much B field goes through a surface".  this
illustrates that moving magnets are the key.  if the magnet is
stationary, flux is not a function of time.  so it's derivative is 0.
if the derivative is 0, EMF is 0.

> Magnetic fields, can move electrons. (Ever made your
> own electromagnet by wrapping wire in a cyll like a spring around a
> screwdriver, and apply a DC current through the wire?)
 
changing magnetic fields produce a non-conservative electric field,
which can accelerate both stationary and non-stationary charges.

static magnetic field can accelerate *only* electrons which are moving
in a direction that's non-parallel to the magnetic field.

> Once you can convince yourself of the impact of EMI on a CRT with your own
> magnets and see how distance plays a very strong hand in it wit the source
> and destination, then you may be able to accept other EM interference as a
> possible problem. I do not recall all of the equations or constants
> (physics was many years ago), but I seem to recall it being something like
>   q(1)q(2)
> K---------- = F
>     r^2
 
that's the force that one stationary charge has on another stationary
charge.  i think the relationship here might be:

F = q(E = v cross B)

which gives the force on a moving electron due to E and B fields in SI
units.

the distance relationship you're looking for is actually in the
calculation of B, via the biot-savart law:

B = integral  I dl cross r
               ------------
                  r^3

so B itself has a 1/r^2 relationship itself.  when you compute this for
a line charge, it turns out that B is a function of 1/r.  that is, B
drops off with 1/distance from the wire causing the B field.

pete

ps- at one time in my life, i really did do more physics than computers.
:)
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