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Re: [Phys-l] drop magnet through loop



On 02/23/2009 07:35 AM, Paul Lulai wrote:

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.

If I'm reading that right, the hypothesis is that the "starting" point
coincides with the "greatest slope" point.

Are you sure that's always true?

I'm pretty sure it's _never_ true for any physically plausible
flux-versus-time curve.

If the magnet drops with a steady downward velocity, you can't
even define a "starting" point.

More generally, if we assume the magnet moves under the influence
of a _finite_ force -- which seems like an exceedingly mild, reasonable
assumption -- then the flux is a smooth function. By smooth I mean
infinitely differentiable, i.e. having an Nth derivative for all N.

Hint: φ(x) is infinitely differentiable and x(t) is infinitely
differentiable. Hint: chain rule.

Note: For simplicity let's assume the magnet passes through the
_interior_ of the loop, without being sliced by the loop.
Again this seems mild and reasonable. This is to avoid picky
discussions about slicing elementary particles.

Bottom line: there simply cannot be any "starting point" where the
curve goes from hump=0=constant to large slope.

As Carl M. suggests: Draw the curve.