Re: [Phys-L] amusing electrostatics exercise

[Jeffrey Schnick <JSchnick@Anselm.Edu>]

In the two skinny wire model, find the magnetic field due to each wire as if it were the only wire.  For one wire of infinite length there is enough symmetry to get the magnitude and direction of the magnetic field at all points in space not on the skinny wire.  Do the coordinate transformation needed to get both results in the same coordinate system.  Add the results.  The result is only appropriate for points in space outside the surface of the original wire.

> -----Original Message-----
> From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of John Denker
> Sent: Thursday, February 28, 2013 12:25 AM
> To: Phys-L@Phys-L.org
> Subject: Re: [Phys-L] amusing electrostatics exercise
>
> On 02/27/2013 02:45 PM, Bruce Sherwood wrote:
> >  At the same
> > location as before, use Ampere's law to calculate the vector magnetic
> > field at that location.
>
> How do you do that?
>
> The only Ampère's law of which I am aware allows us to calculate the
> /average/ field, averaged over some specified loop.  I do not see how to use
> it to calculate the "vector magnetic field" at any "location" ... especially given
> that the problem expressly said that the hole was "non co-axial".  That rules
> out the the sort of symmetry that might allow us to infer a local value from
> the average value.  The problem did not suggest any other symmetry, so the
> only reasonable interpretation I can imagine is that the situation is not
> symmetrical.
>
> Also, the problem explicitly asked for "the mag. field" not some average over
> the field.  I say again, there cannot possibly be any simple solution.
> Counterexamples abound.  A hole on the left side is not equivalent to a hole
> on the right side.  The current knows the difference.  The field knows the
> difference.
>
> _______________________________________________
> Forum for Physics Educators
> Phys-l@phys-l.org
> http://www.phys-l.org/mailman/listinfo/phys-l