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

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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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