97.
(a) The energy density is
u
B
=
B
2
e
2µ
0
=
(50
× 10
−6
T)
2
2 (4π
× 10
−7
H/m)
= 1.0
× 10
−3
J/m
3
.
(b) The volume ofthe shell ofthickness h is
V ≈ 4πR
2
e
h, where R
e
is the radius ofthe Earth. So
U
B
≈ Vu
B
≈ 4π(6.4 × 10
6
m)
2
(16
× 10
3
m)(1.0
× 10
−3
J/m
3
) = 8.4
× 10
15
J .