5.39 In terms of the dc current I, how much magnetic energy is stored in the
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 of the outer
conductor is 10 cm?
Solution: From Eq. (5.99), the inductance per unit length of an air-ﬁlled coaxial
cable is given by
µ0
b
L′ =
(H/m).
ln
2π
a
Over a length of 3 m, the inductance is
L = 3L′ =

3 × 4π × 10−7
10
ln
2π
5

= 416 × 10−9

(H).

From Eq. (5.104), Wm = LI 2 /2 = 208I 2 (nJ), where Wm is in nanojoules when I is in
amperes. Alternatively, we can use Eq. (5.106) to compute Wm :
Wm =

1
2

V

µ0 H 2 d V .

From Eq. (5.97), H = B/µ0 = I/2π r, and
Wm =

1
2

3m

2π

b

z=0 φ =0 r=a

µ0

I
2π r

2

r dr d φ dz = 208I 2

(nJ).

