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[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/