Vernier Software & Technology

# The Magnetic Field of a Permanent Magnet

## Introduction

A bar magnet is called a dipole because 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, Baxis (measured in tesla), of an ideal dipole measured along its axis is

${B_{axis}} = \frac{{{\mu _0}}}{{4\pi }}{\text{ }} \frac{{2\mu }}{{{d^3}}}$

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 an 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.

In this experiment, you will examine how the magnetic field of a small, powerful magnet varies with distance, measured along the axis of the magnet. A Magnetic Field Sensor will be used to measure the magnitude of the field.

Simple laboratory magnets are approximately dipoles, although magnets of complex shapes will exhibit more complex fields. By comparing your field data to the field of an ideal dipole, you can see if your magnet is very nearly a dipole in its behavior. If it is nearly a dipole, you can also measure its magnetic moment.

## 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.
• Determine the magnetic moment of a magnet.

## Sensors and Equipment

This experiment features the following Vernier sensors and equipment.

You may also need an interface and software for data collection. What do I need for data collection?

## Physics with Vernier

See other experiments from the lab book.

 1 Graph Matching 2A Back and Forth Motion 2B Back and Forth Motion 3A Cart on a Ramp 3B Cart on a Ramp 4A Determining g on an Incline 4B Determining g on an Incline 5 Picket Fence Free Fall 6 Ball Toss 7 Bungee Jump Accelerations 8A Projectile Motion (Photogates) 8B Projectile Motion (Projectile Launcher) 9 Newton's Second Law 10 Atwood's Machine 11 Newton's Third Law 12 Static and Kinetic Friction 13 Air Resistance 14 Pendulum Periods 15 Simple Harmonic Motion 16 Energy of a Tossed Ball 17 Energy in Simple Harmonic Motion 18A Momentum, Energy and Collisions 18B Momentum, Energy and Collisions 19A Impulse and Momentum 19B Impulse and Momentum 20 Centripetal Accelerations on a Turntable 21 Accelerations in the Real World 22 Ohm's Law 23 Series and Parallel Circuits 24 Capacitors 25 The Magnetic Field in a Coil 26 The Magnetic Field in a Slinky 27 Electrical Energy 28A Polarization of Light 28B Polarization of Light (Rotary Motion Sensor) 29 Light, Brightness and Distance 30 Newton's Law of Cooling 31 The Magnetic Field of a Permanent Magnet 32 Sound Waves and Beats 33 Speed of Sound 34 Tones, Vowels and Telephones 35 Mathematics of Music

### Experiment 31 from Physics with Vernier Lab Book

#### Included in the Lab Book

Vernier lab books include word-processing files of the student instructions, essential teacher information, suggested answers, sample data and graphs, and more.