Re: [Phys-l] induced electric field

[Philip Keller <PKeller@holmdelschools.org>]

I'm in over my head...but I want to re-ask my question, and then I can work on the answer on my own:

"In a region in space where the magnetic field is steadily increasing at 1 T/s in the z-direction.  A proton is released from rest at the point with (x,y,z) coordinates (1,0,0) .  What is the magnitude and direction of the force that the proton experiences as a result of this changing field?"

Is this an answerable question as is or do I have to specify the boundary conditions that give rise to the increasing magnetic field?  If it is answerable as is, what is the answer?! And why did the coordinates of the location matter?

Sorry if I am being obtuse.  It isn't willful.

> -----Original Message-----
> From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
> bounces@carnot.physics.buffalo.edu] On Behalf Of John Mallinckrodt
> Sent: Monday, November 23, 2009 4:38 AM
> To: Forum for Physics Educators
> Subject: Re: [Phys-l] induced electric field
>
> On Nov 22, 2009, at 8:36 PM, John Denker wrote:
>
> > I think the shoe is on the other foot.  Some folks are
> > assuming without proof -- indeed without evidence -- that
> > the squarish solution exists.
> >
> > ... proponents of squarish solutions are encouraged
> > to exhibit some such thing, in specific and formal terms,
> > and show that it solves the relevant Maxwell equation in
> > the given situation.  I don't think it exists:  too much
> > curl near the corners of the "square" and not enough
> > elsewhere.
>
> Well, in fact, I actually did do some numerical calculations based on
> a Biot-Savart-like transformation of Faraday's law and they clearly
> do support the "squarish solution."
>
> It shouldn't surprise anyone that the solution we seek is identical
> in form to that for the B-field produced by a uniform current density
> within a region having a square cross section.  For a quick and dirty
> solution I set up a spreadsheet with a 20x20 array of 400 "wires"
> carrying "current" in the +z direction and used it to calculate the
> resulting field at arbitrary positions in the x-y plane.  Inside the
> square, the solution is a little too too susceptible to the varying
> distance to the nearest wire to be reliable, but outside the solution
> is quite stable and smooth.  For a radius of 15 units, I calculated
> the B-field every 3 degrees from 0 to 45 degrees and found that the
> field is purely tangential at 0 and 45 degrees as expected, but has a
> positive radial component for angles in between (and a negative
> radial component for angles between 45 and 90 degrees.)  In addition,
> I found that the field increases monotonically in magnitude as one
> moves from 0 to 45 degrees. These are exactly the signatures one
> would expect for the squarish solution and I would further expect the
> boundary conditions to require the "squarish solution" to propagate
> into the inner region.
>
> John Mallinckrodt
> Cal Poly Pomona
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