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C:\User\Teaching\505506\F10\HW09sol.doc
PHY 505
Classical Electrodynamics I
Fall 2010
Homework 9 with solutions
Problem 9.1
(to be graded of 20 points). A straight thin wire with dc current
I
runs in the plane
separating two semispaces filled with different uniform, soft magnetic materials, with different values
(
1
and
2
) of the magnetic permeability. Find the spatial distribution of fields
B
and
H
, and
magnetization
M
.
Solution
:
Solution
: In class, we have calculated the magnetic field
induced by a straight wire in free space – see Eq. (5.20). From Sec. 5.7
we know that if the free space is replaced by a
uniform
material with
0
, the field increases proportionally to
, so that for the straight wire
n
B
2
I
,
where {
,
,
z
} are the standard cylindrical coordinates with vector
n
z
along the direction of the current, and the origin placed at some point of the wire.
Let us try to look for the solution of our problem (see Fig. on the right showing its crosssection)
in the similar form, but with some effective permeability
ef
:
2
,
ef
I
B
B
n
r
B
,
so that
r
n
r
n
r
H
ef
2
I
B
,
where
(
r
) is the local permeability, equal to either
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 Fall '08
 Stephens,P
 Current, Magnetism, Work, Magnetic Field

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