Page 524 - Electromagnetics

A z F 1 (k z z) + B z F 2 (k z z), k z
= 0,
Z(z) = (D.33)
a z z + b z , k z = 0.

 jξ
e

 − jξ

e
F 1 (ξ), F 2 (ξ) = (D.34)
sin(ξ)



cos(ξ)
Cylindrical coordinate system

Coordinate variables
u = ρ, 0 ≤ ρ< ∞ (D.35)
v = φ, −π ≤ φ ≤ π (D.36)
w = z, −∞ < z < ∞ (D.37)

x = ρ cos φ (D.38)
y = ρ sin φ (D.39)
z = z (D.40)

2
ρ = x + y 2 (D.41)
y
−1
φ = tan (D.42)
x
z = z (D.43)
Vector algebra
ˆ ρ = ˆ x cos φ + ˆ y sin φ (D.44)
ˆ
φ =−ˆ x sin φ + ˆ y cos φ (D.45)
ˆ z = ˆ z (D.46)

ˆ
A = ˆρA ρ + φA φ + ˆ zA z (D.47)

(D.48)
A · B = A ρ B ρ + A φ B φ + A z B z

ˆ

ˆ ρ φ ˆ z

(D.49)

A × B = A ρ A φ A z

B ρ B φ B z

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