Fundamentals of Applied Electromagnetics (7th Edition) by Fawwaz T. Ulaby
Author:Fawwaz T. Ulaby [Ulaby, Fawwaz T.]
Language: eng
Format: epub
Publisher: Pearson
Published: 0101-01-01T00:00:00+00:00
* * *
248
CHAPTER 5
MAGNETOSTATICS
of the magnetic fields due to dl and dl add because they are
P = (R, θ, φ) in a spherical coordinate system, with R the
in the same direction, but their r components cancel because
distance between the center of the loop and point P , we would
they are in opposite directions. Hence, the net magnetic field
have obtained the expression
is along z only. That is,
I
d
cos θ
H = ˆz dHz = ˆz dH cos θ = ˆz
dl.
(5.32)
4π(a2 + z2)
m
H =
( ˆR 2 cos θ + ˆθ sin θ)
(5.38)
4πR3
For a fixed point P (0, 0, z) on the axis of the loop, all quantities
(for R a).
in Eq. (5.32) are constant, except for dl. Hence, integrating
Eq. (5.32) over a circle of radius a gives
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