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Re: Induced E Fields in Solenoids



On Fri, 17 Jan 1997, Leigh Palmer wrote (in response to my previous post
regarding the establishment of electric fields in a conducting loop
immersed in the time-varying magnetic field within a solenoid):

I don't understand why you treat this as a transient effect. It should
hold in steady state if the applied B field increases linearly in time.
That is easier for me to understand than the transient problem.

To this I will add that the Hall effect must also be taken into account
somehow; I don't know how!

Perhaps I didn't make myself clear. Although I confess that I had some
trouble understanding earlier portions of your post that I haven't
reproduced here, I suspect that we are ultimately in agreement.

Anyway (for those not yet sick of this thread) ...

I was focusing on the brief period of time following a *change* in the
rate of change of B within the solenoid. Specifically I had in mind a
situation in which B is zero (or at least constant) for some period of
time and then abruptly begins to change linearly with time.

*Just* after the abrupt change in dB/dt, currents will be driven
exclusively by the induced E field and (as I take you to be pointing out
with your reference to the Hall effect) diverted by the magnetic field.
Because these currents will generally have a component transverse to the
"loopy dimension" of the loop, they will be driven from and to various
regions on the surface creating nonzero surface charge densities there.
One doesn't need to know any details to see that this surface charge
configuration--whatever it is--will impede its own continuing build up and
quickly establish an electric field configuration that self-consistently
guides a steady-state, divergenceless current around the loop in the
direction of the induced emf.

Of course, once the requisite E fields have been established there is no
further problem, but my point in examining the transients was to answer
the question as to how these fields come about in the first place. I
understood Ron to be asking about off-axis loops specifically because, at
some points in such loops, the current can flow in a direction opposite
that of the induced electric field.

Regarding the Hall effect: The fact that it will change with time (along
with B) simply means that, even after the initial transient process is
finished, there will be an ongoing requirement for minor, continuous
readjustment of the surface charge configuration. I would consider this a
"second order effect" that modifies the details but not the essence of the
transient process of interest.

John
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A. John Mallinckrodt email: mallinckrodt@csupomona.edu
Professor of Physics voice: 909-869-4054
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