51.
(a) The magnitude of the magnetic dipole moment is given by µ = N iA, where N is the number of
turns, i is the current, and A is the area. We use A = πR
2
, where R is the radius. Thus,
µ = N iπR
2
= (300)(4.0A)π(0.025 m)
2
= 2.4 A
·m
2
.
(b) The magnetic field on the axis of a magnetic dipole, a distance z away, is given by Eq. 30-29:
B =
µ
0
2π
µ
z
3
.
We solve for z:
z =
µ
0
2π
µ
B
1/3
=
(4π
× 10
−7
T
·m/A)(2.36 A·m
2
)
2π(5.0
× 10
−6
T)
1/3
= 46 cm .