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Re: [Phys-l] drop magnet through loop

Hello.

I feel I am getting closer to seeing the flux / voltage curves. I still have a question. I attempted to send a link through GE's Imagination Cubed site. We'll see if it works it should come through separately.

My question: I can see how the flux vs time plot of a magnet falling through a hoop would be a single hump.
If we take the derivative to get voltage, would the point where the 'hump' begins being non-zero be the region of largest voltage? That seems odd to me. However, that would be where the slope would be greatest.


Paul Lulai
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-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of Carl Mungan
Sent: Thursday, February 19, 2009 11:30 AM
To: phys-l@carnot.physics.buffalo.edu
Subject: [Phys-l] drop magnet through loop

So I have a loop of wire parallel to Earth. I drop a magnet through the loop.
The magnet is lined up with N on top and S on bottom (so S goes through the
loop first).
If I were to qualitatively graph the flux vs time, and current vs time I'd get
(would I get?):

Part 1: S is far away to S / N magnet bisect the loop.
Flux goes from zero (or really really small) to a maximum (when S pole is in
center of loop) and then back to zero when the magnet is bisected by loop
(weakest part of magnetic field).

Part 2: S / N bisect loop to N is far away.
Flux goes from zero to maximum (when N pole is in center of loop) to zero when
N is really far away.

When this is graphed, is this like a 2 humped camel with both humps up, or is
this more like a sine curve with one hump up and one hump down?
How would we get the up vs down (+ vs -) from Flux = BA (where would the
negative come from)?
When we rotate a magnet in the place of a coil, the angle changes and rotates
through the 2rpi. The cosine would give us +/-. Since we are not
rotating, it
would appear that we could choose if we want it to be + or - the entire fall.

So-
Would flux be a two humped camel?
Would the two humps be both up, or could you explain how to make one
up (+) and
one down (-)?

To illustrate Schnick's response ("Flux is max when magnet is
bisected by the loop") I recommend you sketch magnetic field lines
for a bar magnet. Note that any given field line (except one right on
the axis of symmetry of the bar magnet assuming it's cylindrical) is
nearest the axis on the plane midway between the poles inside the
magnet and then loops away and around outside the magnet. When it
eventually crosses the mid-plane again, it will be at the largest
distance away from the axis of symmetry that it ever gets. I hope
you're drawing a sketch, so you can follow my wordy explanation.
Finally, by symmetry the field line half-loop above the mid-plane
looks identical to its half-loop below the mid-plane.

Okay then. If a field line crosses into the loop (say it just crosses
the loop's circumference when the mid-plane of the magnet is a
vertical distance y above the loop), then the field line will only
cross back out of the loop when the magnet is vertical distance y
below the loop. Consequently the flux monotonically increases until
the midplane of the magnet crosses through the loop, just as Schnick
asserted. So it will be smoothly single-humped.

Now you can take its derivative to get emf which is smoothly
two-humped with a zero right at the mid-plane y=0.

Hope I haven't been too long-winded. Carl
--
Carl E Mungan, Assoc Prof of Physics 410-293-6680 (O) -3729 (F)
Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-5002
mailto:mungan@usna.edu http://usna.edu/Users/physics/mungan/
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