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Re: [Phys-L] amusing electrostatics exercise

Ampere's law for axial symmetry lets you get the magnetic field inside a
wire as well as outside, so you could if you wish calculate the field at
all locations.

Bruce


On Thu, Feb 28, 2013 at 8:26 AM, Jeffrey Schnick <JSchnick@anselm.edu>wrote:

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.

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