Vernier Software and Technology
Vernier Software & Technology

The Magnetic Field of a Permanent Magnet

Figure from experiment 31 from Physics with Vernier

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.

Additional Requirements

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

Standards Correlations

See all standards correlations for Physics with Vernier »

Physics with Vernier

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2BBack and Forth Motion
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3BCart on a Ramp
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4BDetermining g on an Incline
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6Ball Toss
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8AProjectile Motion (Photogates)
8BProjectile Motion (Projectile Launcher)
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10Atwood's Machine
11Newton's Third Law
12Static and Kinetic Friction
13Air Resistance
14Pendulum Periods
15Simple Harmonic Motion
16Energy of a Tossed Ball
17Energy in Simple Harmonic Motion
18AMomentum, Energy and Collisions
18BMomentum, Energy and Collisions
19AImpulse and Momentum
19BImpulse and Momentum
20Centripetal Accelerations on a Turntable
21Accelerations in the Real World
22Ohm's Law
23Series and Parallel Circuits
24Capacitors
25The Magnetic Field in a Coil
26The Magnetic Field in a Slinky
27Electrical Energy
28APolarization of Light
28BPolarization of Light (Rotary Motion Sensor)
29Light, Brightness and Distance
30Newton's Law of Cooling
31The Magnetic Field of a Permanent Magnet
32Sound Waves and Beats
33Speed of Sound
34Tones, Vowels and Telephones
35Mathematics of Music

Experiment 31 from Physics with Vernier Lab Book

<i>Physics with Vernier</i> book cover

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