Re: [Phys-l] drop magnet through loop

[Carl Mungan <mungan@usna.edu>]

> My question:  I can see how the flux vs time plot of a magnet 
> falling through a hoop would be a single hump.

Good.

> 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.

I don't think so. The slope is largest about halfway up the leading edge.

Draw a smooth bell-shaped curve. For simplicity, make it peak at x=0 
and be symmetric when reflected about the y-axis. Its slope is zero 
at three points: right at x=0 where it's horizontal and at + and - 
infinity where it's y-value is zero.

Moving from negative to positive infinity, the slope starts out zero, 
increases continuously until it reaches an inflection point about 
halfway vertically up to the peak and then it decreases continuously 
to zero at x=0 and smoothly continues to decrease to negative values, 
with a maximum negative value symmetrically located relative to the 
positive maximum, when you're again about halfway down from the peak. 
Thereafter the slope increases back to zero. The overall emf curve is 
odd, with a positive peak +E at some negative value -x, and a 
negative peak -E at +x symmetrically (inversion symmetry). It looks 
sort of like one full cycle of a sine curve. (Or you could change the 
overall sign so you have -E at -x and +E at +x if you flip either the 
magnet or the voltmeter connections around.) -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/