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Re: Graphing by Hand



Just for fun now, see if you can make a sketch of this graph....

A small bar magnet, north pole down, is held 0.5 meter above the
]center of a vertical air core solenoid. The solonoid is 0.5 meter
long and sufficiently wide to allow the bar magnet to fall through
without touching its coils. A voltmeter (or an oscilloscope) is
attached to the ends of the solenoid coils.

Sketch a voltage vs time graph from the time that the magnet is
released, falls freely through the solenoid and emerges 0.5
meter below the solenoid bottom.

Herb Gottlieb from New York City
(Where solving this problem was one of the most enjoyable
and challenging highlights of our Advanced Placement Physics Course)

Great problem, Herb! I find it sufficiently challenging that I have
been thinking about it for five* minutes now, and I'm still unsure
that I know the answer. I've got the end passages qualitatively
right, but I'm unsure about the stretch in between, when the magnet
is falling (and accelerating) through the center portion of the
solenoid. I'm now convinced that there will be a very small DC
offset from zero over that stretch, but I may change my mind in
five minutes! The solution, as I see it, is best understood in
terms of a sum of the signals from a series of voltage-vs-time
curves for passages through single loops. In such a case the
voltages are a series of the characteristic s-waves with amplitudes
increasing in time as the magnet's speed increases. (I don't know
what else to call that shape other than s-wave.) In that case the
solution for the time between the ends will be a small DC offset
in the same sense as the first excursion of the voltage.

I hope you will make the solution as you see it available to all,
together with your students' best insights. The problem is still
sufficiently challenging that I will be thinking about it all day.
Of course I could simply calculate the result, but in my opinion
that would be cheating, or I *could* perform the experiment, and
that would not be cheating!

Herb Gottlieb from New York City
(Where solving this problem was one of the most enjoyable
and challenging highlights of our Advanced Placement Physics Course)

Leigh

*twenty minutes by the time I finished typing this.