Magnetic Moment Question

Question

A student makes a short electromagnet by winding 300 turns of wire around a wooden cylinder of diameter 5.0 cm. The coil is connected to a battery producing a current of 4.0 A in the wire.

a. What is the magnetic moment of the device?

b. At what axial distance will the magnetic field of this dipole have the magnitude 5.0 micro-T?

Answer 1

a.

►  M = I N A = 4 × 300 × π d² / 4 = 4 × 300 × π × 0.05² / 4 = 2.356 A·m².

b.

For a short coil, magnetic field at distance r from plane of coil having N turns, radius a, current I, is given by B = µo/2 · N I a² / r³ ; solving for r,

►  r = ³√ (µo/2 · N I a² / B) = ³√ [ (4π E-7) / 2 × 300 × 4 × 0.05² / 5 E-6 ] = 0.7224 m = 722.4 mm.