A student makes a short electromagnet by winding 300 turns of wire around a wooden cylinder of diameter d 5.0 cm. The coil is connected to a battery producing a current of 4.0 A in the wire. (a) What is the magnitude of the magnetic dipole mo - ment of this device? (b) At what axial distance d will the mag - netic field have the magnitude 5.0 mT (approximately one-tenth that of Earth's magnetic field) ?

A) μ = A. m²

B) z = 0.46m

Explanation:

A) Magnetic dipole moment of a coil is given by; μ = NIA

Where;

N is number of turns of coil

I is current in wire

A is area

We are given

N = 300 turns; I = 4A; d = 5cm = 0.05m

Area = πd²/4 = π (0.05) ²/4 = 0.001963

So,

μ = 300 x 4 x 0.001963 = 2.36 A. m².

B) The magnetic field at a distance z along the coils perpendicular central axis is parallel to the axis and is given by;

B = (μ_o•μ) / (2π•z³)

Let's make z the subject;

z = [ (μ_o•μ) / (2π•B) ] ^ (⅓)

Where u_o is vacuum permiability with a value of 4π x 10^ (-7) H

Also, B = 5 mT = 5 x 10^ (-6) T

Thus,

z = [ (4π x 10^ (-7) •2.36) / (2π•5 x 10^ (-6)) ]^ (⅓)

Solving this gives; z = 0.46m =