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Re: [Phys-l] induced electric field



On 11/23/2009 08:34 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?

You need to specify the region. The point (1,0,0)
could be at the far left of the region, or the middle
of the region, or the far right of the region ...
and it matters. A B field that is changing at a
uniform rate does not produce a uniform E field.
It can't. The Maxwell equation forbids it. A
uniform E field would have no curl at all, not the
curl required by the Maxwell equation.

Minor point: Technically, as part of the boundary
conditions or otherwise, you also need to say that
the changing magnetic field is the only field in the
problem. Everybody assumes that's what was intended.

If it is answerable as is, what is the answer?! And why did the
coordinates of the location matter?

Questions about "why" are often unanswerable. In
most cases, the laws of physics tell us what happens
without really telling us "why" it happens.
http://www.av8n.com/physics/causation.htm
When somebody asks "why ..." I always hope they intended
to ask "how do we know ..." which is an easier question
to answer.

In this case, we know something about how the E field
behaves because have well known solutions for the case
of a circular region. The solution
E = x j + y i
is easy to derive and even easier to verify. The field
is highly nonuniform, as you can see in this picture:
http://www.av8n.com/physics/non-grady.htm#fig-betatron

The solution for a square solenoid is qualitatively
similar but not the same. Position within the field
still matters.

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

You have nothing to apologize for. It's a perfectly
reasonable question. I've given some lousy answers,
but the quality of the answer is no reflection on
the quality of the question.