Re: Induced E Fields in Solenoids

[Ron Curtin <curtin@oven.ccds.charlotte.nc.us>]

On Wed, 15 Jan 1997, Leigh Palmer wrote:

> > Thanks to Gene for the response to my question.  Is there any reason that
> > the circle has to be coaxial with the soleniod?  If I choose a circle that
> > is not coaxial with the solenoid --- if for example it doesn't include the
> > axis of the solenoid, I could use Lenz's Law to make a case for an induced
> > current or E-field in the opposite direction.
>
> I don't know if my posting on this appeared. In it I pointed out that
> the E field must share the symmetry of the B field. No circle other
> than a coaxial circle does so. If one picks an arbitrary circle, then
> yet any other circle will do, including any circle that intersects
> the first arbitrary circle in one point. Since this degree of
> arbitrariness has been allowed, the direction of the E field at the
> point of intersection is indeterminate; thus it must vanish! Only by
> constraining the circles to be coaxial with the solenoid can we avoid
> this possibility of intersecting circles and thus obtain a nontrivial
> result.
>
> Leigh
I understand that I can define the direction of the E field by
considering a loop in the solenoid coaxial with the solenoid and then use 
Lenz's Law to find the direction of the induced current in the loop and
then use this direction as the direction of the E field.  I will then
have defined the direction of the induced Electric Field at a specific
point in the solenoid.  My real problem is this:  I can now put a metal
loop in the solenoid that passes through that point and is not coaxial to 
the solenoid in such a way that the induced current in that loop
(according to Lenz's Law) is opposite to the direction predicted by my
original coaxial loop.  Does that mean that the current in this new loop
is opposite to the direction of the E field?> >