Re: Jumping Ring Demo

[Doug Craigen <dcc@CYBERSPC.MB.CA>]

Rick Morra wrote:
> I have a problem with all the explanations given for the phenomenon
> except that given by Doug Craigen:
>
> The apparatus that I have in lab is asymmetrical. The the coil is not
> inside the ring but below it. There is a soft iron core which couples
> the coil and the jumping ring. The ring jumps when an AC source is
> connected to the coil.
>
> Suppose the coil were oriented with a horizontal axis, and the ring
> were placed around the center of the coil. When AC current is applied
> to the coil, which way would the ring jump, left or right?
>
> It would appear to me that due to (perfect?) symmetry it wouldn't jump
> either way. This implies to me that the phenomenon has something to do
> with the gradient of the field created by the coil.
>
> In Martha Trakat's original question she mentioned trying to analyze
> the effect of the gradient. The requirement of a gradient was
> mentioned by Doug Craigen in his response.
>
> I would appreciate if someone would tell me where my thoughts are
> wrong or if someone would expand on Doug's explanation. I don't know
> if the references given by Karl Trappe deal with this; I don't have
> easy access to old issues of AJP.

Since my name is all over this, I guess I should respond.

I haven't read all those AJP articles, all I know is that when I did the
experiment with 2nd year classes at the U of Waterloo (in my grad
student days), I found the written materials inadequate to answer all
the questions.  Questions about why there would be **some sort of** net
effect weren't too hard - they only required showing that it comes from
phase effects.  The product of I and B at any spot on the loop would
average to zero if you just have sin(wt)*cost(wt), but with
sin(wt)*cos(wt+delta), there is a non-zero average for non-zero delta.
This then takes us to questions like why the rings jump to different
heights depending on how many we put on ("with two rings, we double the
mass, and double the current - hence double the force, so
acceleration=force/mass should be the same shouldn't it?").

The more challenging question was "how does the ring know which way to
move?"  For this I couldn't find any satisfactory explanation available,
but with some digging was able to satisfy myself that I had a correct
answer.  Basically, any current loop experiences no net force, only
torques in a uniform external field.  Net forces only arise due to
gradients in the external field.

Here's one way to think about it:
Use an electric-like model for a dipole - a north and a south pole
separated by a tiny distance - what will happen?
In a constant field it will rotate such that the north pole faces
"south" and the south pole faces "north". The two poles are pulled
equally in opposite directions. Now suppose that there is a Gradient ir
the field... there will be a greater pull on one of the poles than on
the other, so a net translational force. *** Note, this is only
provided as a way of thinking about what happens, the math for a current
ring in a magnetic field shows the same thing. ***
Unfortunately the only reference I have at my fingertips right now to
point you to is inaccessible to many members of this list: Classical
Electrodynamics, 2nd Edition, by Jackson, section 5.7 "Force and Torque
on and Energy of a Localized Current Distribution in an External
Magnetic Induction". The linear force for any spot in the distribution
obeys:
F = Gradient(moment.of.the.distribution "dot.product" B)
or, F = del(m.B)

Perhaps the following illustration can help somewhat:
  ^
  | B

----> dI

We have a current segment within a region of uniform magnetic field.
What direction is the force?  It is normal to the face of your monitor.
It is NOT in the direction of B.  Furthermore, if this current element
is part of a planar current loop normal to the magnetic field, then on
the whole loop there is a corresponding equal and opposite horizontal
force on the other side.  However, this can be an unstable equilibrium -
dpending on the direction of I, since if we tilt the loop a bit there
will be a torque.  Note though that there is not going to be a force in
the direction of B, only a torque.

So, my conclusion is that there is a Gradient in the magnetic field
along the iron core, and naturally we expect there to be - magnetic
field lines will be "leaking out" along its length.


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Doug Craigen
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