Re: [Phys-L] amusing electrostatics exercise

[John Denker <jsd@av8n.com>]

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.