Re: [Phys-l] drop a metal cylinder through a solenoid

[brian whatcott <betwys1@sbcglobal.net>]

On 3/24/2012 9:11 PM, Carl Mungan wrote:
> Okay I made some rough estimates. Here's what I came up with.
>
> First, forget about drift velocity. That should be replaced by velocity of the bob. Second, John Denker off-list mentioned I should also consider the 0.5CV^2 energy, but as best as I can tell that term is negligible, because C is so tiny (cf. numbers below).
>
> Numbers (dropping factors of 2 or smaller):
>
> magnetic field B = 100 gauss = 0.01 T
> drop bob from an initial height L = 5 cm
> bob is a cube of side length d = 1 cm
> bob is made of Al which has resistivity p = 3e-8 ohm-m
> permittivity of free space e0 = 9 pF/m
> average speed of bob v = sqrt(g*L)
>
> motional emf (or Hall voltage) V = B*v*d
> resistance of bob R = p/d
> capacitance of bob C = e0*d
>
> dissipated energy E during one-quarter cycle = (V^2/R)*(L/v)
>
> That works out to be B^2 g^0.5 L^1.5 d^3 / p = 1 uJ
>
> compared to mechanical energy of mgL = 1 mJ (Al is 2.7 g/cm^3)
>
> i.e. lose about 0.1% per quarter cycle. (And again, this continues only because the swinging velocity is ac not dc.)
>
> So indeed, the damping is small. -Carl
>
> ---
> Carl E Mungan, Assoc Prof of Physics  410-293-6680 (O) -3729 (F)
> Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-1363
> mailto:mungan@usna.edu     http://usna.edu/Users/physics/mungan/
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Congratulations to Carl, for setting out numbers for an estimate.
 This is not so easy - and so (I suppose) is conspicuous by
its absence from most posts to the list.

Brian W