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Discussion Question 9A
P212, Week 9
Ampere’s Law in a Nutshell
Ampere’s Law is the magnetic analogue of Gauss’ Law.
•
Gauss’ Law relates the integral of the electric field through a
closed “Gaussian surface
” to the total charge
enclosed by that
surface.
•
Ampere’s Law relates the integral of the magnetic field around a
closed “Amperian loop
” to the total current
enclosed by that loop.
Just like Gauss’ Law, Ampere’s Law provides the simplest method for determining the magnetic
field of a known current distribution … but it can
only
be used in a practical way if the problem
has
enough symmetry
.
It all boils down to choosing a suitable
Amperian loop
.
The
mathematical curve we choose has to have these properties:
•
The magnetic field must have a constant magnitude
on our curve.
•
The magnetic field must make a constant angle
with our curve (or portions thereof).
Otherwise, we’ll never be able to extract the
B
field we want from that line integral!
The other part of the procedure is finding the
current enclosed
by our Amperian loop:
•
In your mind, imagine that the Amperian curve is a loop of coathanger wire, and
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This note was uploaded on 06/16/2011 for the course PHYS 212 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Kim
 Charge, Magnetism

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