Re: "Faraday's Disk" which started it all

[Robert A Cohen <bbq@ESU.EDU>]

On Tue, 29 Jun 1999, William Beaty wrote:

> Suppose we hang a test-charge over a large, flat magnet on a table (the
> field is vertical.)  If we move this magnet constantly in a straight line
> under the test charge, the charge responds to an e-field, and we would
> also measure the same e-field near that uniformly-moving magnet.  However,
> since the charge is not moving, there is no qVxB force in this situation.
>
> And conversely, if we anchor our magnet to the table, and then move a
> test-charge in a straight line so it passes above the magnet, the charge
> responds to the qVxB force because the charge is moving through a b-field.
> However, since the magnet is not moving with respect to the table and the
> lab, we would measure no electric field in this situation.
>
> I was screwed up about VxB earlier.  Are we now on the same page?

Okay, so now everyone seems to be on the same page...except me!

What still baffles me is how to state, in words, what "V" means in the
expression "E=VxB".

I understand that the magnetic field is dependent upon one's reference
frame.  And, when one gives the magnetic field of a magnet, one assumes
the magnetic field is measured in the frame in which the magnet is
stationary.  And, if the magnet is moving relative to one's frame, one
will measure both an electric and a magnetic field (special relativity).
Thus, it is most technically correct to say that V is "the velocity of the
charge in the frame of reference in which B is measured". (E=VxB also
assumes non-relativistic speeds, I guess)

However, in the first situation given above (stationary charge over moving
magnet), it is implied that V is the velocity of the charge *relative to
the magnet that produces the field* and B is the magnetic field of the
magnet when it is at rest with respect to the observer (as opposed to the
observing frame).

Since I was originally quite confused by the "motion relative to a field"
statements bandied about in posts, I actually like saying that "V" is the
velocity relative to the magnet, rather then the field, with "B" being the
field measured when the magnet is at rest.  But, is such a statement
valid?

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| Robert Cohen               Department of Physics       |
|                            East Stroudsburg University |
| bbq@esu.edu                East Stroudsburg, PA  18301 |
| http://www.esu.edu/~bbq/   (570) 422-3428              |
|                            **note new area code**      |
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