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Re: [Phys-l] induced electric field



Can you elaborate? I don't understand what you say I have shown or how I've shown it. Thanks.

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of curtis osterhoudt
Sent: Tuesday, November 17, 2009 8:50 AM
To: Forum for Physics Educators
Subject: Re: [Phys-l] induced electric field

You have shown -- neatly -- that such a uniform magnetic field (increasing
or not, at least in the quasistatic limit of d << c*t, where d is some
characteristic spatial dimension in the problem) is induced by a boundary
current (for a solenoid, for example, the current in the wires around the B-
field).





________________________________
From: Philip Keller <PKeller@holmdelschools.org>
To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
Sent: Tue, November 17, 2009 6:14:45 AM
Subject: Re: [Phys-l] induced electric field

Is it possible that there can be no such thing as a uniform magnetic field
that is uniformly increasing? The reason I ask is:

Suppose there were such a region and you wanted to know the electric field at
a point in that region. This is a typical textbook problem: if there were a
wire loop, use Faraday's law to find the induced voltage and set that voltage
equal to E x circumference. This is an example problem in many texts. My
question is about the direction of the induced electric field (hard to
explain without a diagram) - presumably it is in the direction of the induced
current. But if you were to move the wire loop, say one diameter to the
right, it would still be in the same uniformly increasing uniform field. So
if the current was clockwise (say) before, it would still be clockwise. But
now the electric field direction at the leftmost point is in the opposite
direction of what it was when that location was the rightmost point of the as-
of-yet-untranslated wire loop. But that means the direction of the induced
electric field caused by a uniformly increasing
uniform field varies with t
he orientation of a wire loop placed in that field!

So either that is OK, or my analysis is wrong, or there is no such thing as a
uniformly increasing uniform magnetic field. But of those three, I have no
idea which is right.


-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of Carl Mungan
Sent: Monday, November 16, 2009 5:03 PM
To: phys-l@carnot.physics.buffalo.edu
Subject: [Phys-l] induced electric field

A standard textbook problem says: Assume a uniform magnetic field (B)
pointing into the page inside a circular region of radius R (and zero
outside of it) and increasing in magnitude at a constant rate
(dB/dt). Find the induced electric field (E) everywhere in space.

For specificity, assume the B field is produced by an ideal solenoid.
One finds by symmetry that E is azimuthal in direction, increasing
linearly from zero for r<R up to (R/2)(dB/dt) in value, and then
dropping off as the inverse square outside the solenoid.

Fine, now what happens if the solenoid is square in cross-section?
(This question was asked by a student.) Say length L on a side, and
still ideal so B uniform inside and zero outside with constant rate
of increase of strength.

Regardless of whether I try the differential or the integral form of
Faraday's law, I don't seem to make much progress. Who can help me
out? If this variation is done in some reference, that would be
helpful too. -Carl
--
Carl E Mungan, Assoc Prof of Physics 410-293-6680 (O) -3729 (F)
Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-1363
mailto:mungan@usna.edu http://usna.edu/Users/physics/mungan/
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
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_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
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_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l