The Magnetic Field of a Permanent Magnet

Introduction

A bar magnet is called a dipole since it has two poles, commonly labeled North and South. Breaking a magnet in two does not produce two isolated poles; each fragment still has two poles. Similarly, two magnets together still exhibit only two poles. Since to our knowledge there are no magnetic monopoles, the dipole is the simplest possible magnetic field source.

The dipole field is not limited to bar magnets, for an electrical current flowing in a loop also creates this common magnetic field pattern.

The magnetic field B_axis (measured in tesla) of an ideal dipole measured along its axis is

where μ₀ is the permeability constant (4π×10^–7 T m/A), d is the distance from the center of the dipole in meters and μ is the magnetic moment. The magnetic moment μ measures the strength of a magnet, much like electrical charge measures the strength of a electric field source. Note that the distance dependence of this function is an inverse-cube function, which is different from the inverse-square relationship you may have studied for other situations.

Objectives

• Use a Magnetic Field Sensor to measure the field of a small magnet.
• Compare the distance dependence of the magnetic field to the magnetic dipole model.
• Measure the magnetic moment of a magnet.