Re: [Phys-l] induced electric field

[John Mallinckrodt <ajm@csupomona.edu>]

As you probably suspect, the question is, indeed, underspecified and,  
thus, unanswerable.  The inadequacy in the problem specification  
might be remedied in more or less difficult ways , e.g., you might  
specify a) some appropriate boundary conditions and the behavior of  
the magnetic field everywhere within (or without) those boundaries or  
b) you might simply specify the electric field at the release point  
since any value is compatible with the given dB/dt.

I think the larger point to be made in this thread is that one should  
not be seduced by the idea that one can use symmetry arguments as  
long as everything "inside some radius" is symmetric.  For instance,  
we can use Gauss' law to find the electric field everywhere in space  
due to a charge of 1.0 Coulomb spread uniformly throughout a 1.0  
meter radius sphere.  Most trivially, we find that the field at the  
center of the sphere vanishes.  But if we take a 1.0 picoCoulomb bite  
out of the very edge of the sphere, the electric field changes  
*everywhere* (except at a very specific point or points within the  
void left by the bite itself), including at the very center of the  
sphere.

John Mallinckrodt
Cal Poly Pomona

On Nov 23, 2009, at 7:34 AM, Philip Keller wrote:

> 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.