Lab 8
Magnetometers

A magnetometer is an instrument used for measuring the strength of a magnetic field. A simple magnetometer can be created from a torsional pendulum by using a nylon thread to suspend a cylindrical bar magnet from a rigid, non-magnetic support. One end of the thread is looped over the support. The other end is fixed to a plastic sleeve of negligible mass that surrounds the magnet.

The goal, today, is to use a torsional pendulum as a simple magnetometer. See Figure 1.

Figure 1. A Torsional Pendulum

Review Theory

A bar magnet suspended in a uniform magnetic field will act as a compass and align itself with the field. When the magnet is rotated slightly it will oscillate about its equilibrium position exhibiting simple harmonic motion. For a small angle of rotation, θ, the restoring torque, τ, is proportional to the angle where:

and the constant of proportionality, κ, is called the torsion constant. The restoring torque is given by:

where, µ, is an intrinsic property of the magnet called its magnetic moment and, B, is the horizontal component of the magnetic field. The period of oscillation of the magnet, T, about its equilibrium position is given by:

where, I, is the moment of inertia of the magnet about its axis of rotation. This equation can be written as:

where, C, is called the pendulum constant:

Although the pendulum constant can be calculated from the moment of inertia and the magnetic moment it can also be determined from the period of oscillation in a known magnetic field. For example, the horizontal component of the magnetic field of the earth, Be. In this case:

Notice that an unknown field strength can be determined from the period of oscillation if the pendulum constant is known, since: