A student makes a short electromagnet by winding 100 turns o

A student makes a short electromagnet by winding 100 turns of wire around a wooden cylinder of diameter d = 7.0 cm. The coil is connected to a battery producing a current of 3.0 A in the wire.

(a) What is the magnitude of the magnetic dipole moment of this device?
A · m²

(b) At what axial distance z » d will the magnetic field of this dipole have the magnitude 5.0 T (approximately one-tenth that of Earth\'s magnetic field)?
cm

Solution

mu = N I A = 100 * 3.0 * (pi * (3.5 * 10^-2)²)

= 1.154 A.m²

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r = cube root (mu₀/2 * N I a² / B)

= cube root [ (4pi * 10^-7) / 2 * 100 * 3 * 0.07² / 5 * 10^-6 ]

= 0.569 m = 56.9 cm