48.
(a) We set z = 0 in Eq. 30-28 (which is equivalent using to Eq. 30-12 multiplied by the number of
loops). Thus, B(0)
∝ i/R. Since case b has two loops,
B
b
B
a
=
2i/R
b
i/R
a
=
2R
a
R
b
= 4 .
(b) The ratio of their magnetic dipole moments is
µ
b
µ
a
=
2iA
b
iA
a
=
2R
2
b
R
2
a
= 2
1
2
2
=
1
2
.