Re: [Phys-L] Magnetic Braking

[John Denker <jsd@av8n.com>]

On 9/24/24 1:45 PM, Zeke Kossover via Phys-l wrote:

> At the Exploratorium, we have put together an exhibit that has two parallel
> columns of strong, not rare earth, permanent magnets. They are
> approximately 4 inches x 8 inches x 1 inch (10 cm x 20 cm x 2.5 cm). We
> drop an aluminum disk between the two sides.
>
> We've arranged them with all the poles on one side
>
> N    S
> N    S
> N    S
> N    S
> N    S
> N    S
> N    S
> N    S
>
> And we have also arranged the magnets with alternating poles like this
>
> N    S
> N    S
> S    N
> S    N
> N    S
> N    S
> S    N
> S    N
>
> The disk falls slower (has a lower terminal velocity) in the alternating
> version.
>
> I'm not sure why. If it isn't my imagination, do you think having it
> alternate more often would make the disk fall even slower?

Interesting question. It's slightly ill-posed, because it depends
on unstated details of the geometry, namely the vertical and
horizontal spacing of the poles.

The interesting case is when the horizontal spacing is small
compared to the vertical distance between poles, so that the field
lines in the alternating configuration have a large horizontal
component (as opposed to just "shorting out" to the neighboring
pole in the vertical direction).

  (If the alternating poles are close together vertically, the
  disk sees no field at all. Not very interesting.)

Next imagine that the disk is made of a huge number of small rings,
like chain mail. Such a ring falling through a uniform field sees
no braking, no force at all (assuming no yaw pitch or roll). The
only change in flux through a ring occurs when the ring is moving
through a region of non-uniform field. If the overall size of the
disk is comparable to the size of the array of magnets, it may be
hard to sort out what's happening.

Bottom line: To maximize braking, you want to have as much spatial
variation as you can get without sacrificing field strength.

Suggestion: Get a disk (or ring) that is small compared to the
overall size of the array of magnets. Attach it to a non-magnetic
handle. Observe what happens when you wiggle it in a region of
uniform field.