H-Field in a region with magnetic susceptibility from an infinite line charge

  • Thread starter FrancisD
  • Start date
  • #1
5
0

Homework Statement



Pollack, Stump - Electromagnetism. Prob. 9.23

A long straight wire carrying current 1 is parallel to the z axis and passes through
the point (a, 0, 0) . The region x > 0 is vacuum, and the region x < 0 is a material
with magnetic susceptibility Xm .
Show that the H-field in the region x < 0 is the same as H that would be produced
by a current 211(2 + Xm) in the wire with the material everywhere; and the H-field
in the region x > 0 is the same as H that would be produced by the combination of
the current 1 in the wire and a current Xm 1 I (2 + Xm) along the line parallel to the z
axis through (-a, 0, 0), with vacuum everywhere. (Hint: Appeal to the uniqueness
theorem. What are the boundary conditions?)



Homework Equations



H = B/μ0 - M

M = χH

∫H dl = I (free, enclosed)


The Attempt at a Solution



Ok, so my first thought was to find the H-field in both regions using ampere's law, but won't I have to find the magnetization to be able to find it in the region with the magnetic susceptibility? What is tripping me up is figuring out to solve it with 2 separate regions. Any initial help to get me started would be great. Thanks
 

Answers and Replies

Related Threads on H-Field in a region with magnetic susceptibility from an infinite line charge

Replies
1
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
1K
Replies
3
Views
8K
Replies
2
Views
4K
Replies
55
Views
9K
Replies
2
Views
721
Replies
2
Views
3K
  • Last Post
Replies
2
Views
3K
Top