Re: Induced E Fields in Solenoids

["Eugene P. Mosca" <mosca@nadn.navy.mil>]

Hi Ron, you said
> I could use some help explaining to my AP students how to find the 
> direction of the induced E field at various points inside a solenoid if 
> the current in the solenoid is increasing or decreasing.  I would 
> appreciate any helpful hints that any of you could offer.  Thanks.
The direction of the induced E field can be determined using Lenz's law.
The argument goes as follows.

Let B denote the field due to the current I in the solenoid.  Consider the
emf induced around a circular path C that is coaxial with the solenoid.
Let S be the flat circular surface bounded by C.  Any change in I causes B
to change--and so causes a change in the flux of B through S.  Any induced
current I' in C produces a second magnetic field B', and in accord with
Lenz's law, the flux of B' through S opposes the change in the flux of B
through S.  This means that if |B| increases on S then B' and B are
oppositely directed, and if |B| decreases on S then B' and B are in the
same direction.  Once the direction of B' is known, the direction of I'
can be determined via the same right hand rule that gave the direction of
B knowing the direction of I.  

The induced emf is the circulation of the induced electric field E.  Thus
E is tangent to C in the direction of the induced current.

I hope this answers your question.

Gene
 
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Eugene (Gene) P. Mosca           Phone 410-293-6659 (Fax 3729)
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