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Re: [Phys-L] amusing electrostatics exercise



On 02/27/2013 12:20 AM, Bernard Cleyet wrote:
What is the mag. field surrounding a large, DC current carrying,
diameter wire with a non co-axial hole thru it. For simplicity
assume infinite length.

bc thinks ridiculously simple if not wet.

Here's a proof that the question is seriously underspecified, and
that there cannot possibly be a simple answer (ridiculously or
otherwise).

a1
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xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx original wire
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a2
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xxxxxxxxxxxx xxxxxxxxxxxxxxx wire with upper notch
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a3
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xxxxxxxxxxxx xxxxxxxxxxxxxxx wire with lower notch
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In the /far field/ these wires will all produce very nearly the
same field, but in the near field, the field near point a2 will
be very different from the field near a3.

====

FWIW if you restrict attention to the /average/ field, averaged
over some fixed loop somewhere outside the original wire, then
notching the wire will have no effect. Ampère's law. However,
the concept of "field" is different from the concept of "average
field".