5.39
DESCRIPTION
problem 5.39 solutionTRANSCRIPT
Problem 5.39 In terms of the dc currentI, how much magnetic energy is stored inthe insulating medium of a 3-m-long, air-filled section of a coaxial transmission line,given that the radius of the inner conductor is 5 cm and the inner radius ofthe outerconductor is 10 cm?
Solution: From Eq. (5.99), the inductance per unit length of an air-filled coaxialcable is given by
L′ =µ0
2πln
(
ba
)
(H/m).
Over a length of 2 m, the inductance is
L = 2L′ =3×4π×10−7
2πln
(
105
)
= 416×10−9 (H).
From Eq. (5.104),Wm = LI2/2 = 208I2 (nJ), whereWm is in nanojoules whenI is inamperes. Alternatively, we can use Eq. (5.106) to computeWm:
Wm =12
∫
V
µ0H2 dV .
From Eq. (5.97),H = B/µ0 = I/2πr, and
Wm =12
∫ 3m
z=0
∫ 2π
φ=0
∫ b
r=aµ0
(
I2πr
)2
r dr dφdz = 208I2 (nJ).