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 .