PURPOSE To investigate the magnetic field distribution of a current carrying conductor, both in magnitude and direction. To measure the Earth’s magnetic field.

EQUIPMENT Helmholtz pair, 5-amp dc power supply, rheostat, reversing switch, jar magnet, dc ammeter, meter stick, compass, stopwatch, half-meter stick.

RELEVANT EQUATION

DISCUSSION

Magnets and Magnetic Poles

The opposite ends or poles of a magnet are designated North-seeking (N) and South-seeking (S), just as the two kinds of electric charge are designated positive (+) and negative (—). As with charge, opposite poles attract each other and like poles repel each other with an inverse square dependence on distance. The effect that a magnet, or group of magnets, has on a pole is conveniently described in terms of the magnetic field B, which is analogous to the description of electric forces in terms of the electric field E.

The magnetic field at a point P due to a magnet is equal to the force exerted by the magnet on a unit North-seeking magnetic pole located at P. Thus, the magnetic field is a vector quantity that can be associated with every point in the vicinity of the magnet. It can be graphically represented by drawing the field lines associated with the magnet, as shown in Fig. 17-1. At any point P, the direction of B is tangent to the field line at P and the magnitude of B is indicated by the spacing of the lines: the closer the lines are spaced, the greater the magnitude of B. The unit of measure for B in the SI system is the tesla (T).

In the case of a C-magnet, the direction of B is from the North-seeking to the South-seeking pole and the lines are more or less equally spaced, which indicates that the magnitude of B is constant throughout the region between the poles. In the case of a bar magnet, the direction and magnitude of B vary throughout the surrounding space in a complicated way. Obviously the magnitude of B is greatest near the poles of the magnet.

The field lines produced by a particular source can be determined by using a small bar magnet, such as a compass needle, mounted on a pivot so that it is free to rotate. The magnet responds to a magnetic field at its location by lining up with the field lines. The reason for this is that an external magnetic field produces a torque t on the bar magnet that is proportional both to the field strength and to the projection of a line perpendicular to the direction of the bar magnet on to the direction of B. Although it sounds complicated geometrically, it can be stated quite simply: the magnetic torque is maximum when the bar magnet is perpendicular to the field line, and zero when it is parallel to it. The torque takes on intermediate values if the magnet’s angle lies between zero and 90° with respect to the direction of B. This situation is reminiscent of the restoring force acting on simple harmonic oscillator. In fact the magnetic torque on the bar magnet is a restoring torque that for small angles can produce simple harmonic oscillations of the bar magnet.

To be more precise, let us draw an arrow from the South-seeking to the North-seeking pole of the bar magnet. This arrow represents the magnetization vector M of the bar magnet. As shown in Fig. 17-2 the magnetic torque on the bar magnet always acts to align M with B. This kind of torque is called a restoring torque because it tends to restore the magnet to the aligned position.

If the bar magnet is already lined up with B, the torque is zero and the magnet will remain in that orientation. If the bar magnet is not initially lined up with B however, the restoring torque will cause the bar magnet to oscillate about the direction of B. The period of oscillation T of the magnet can be shown to be inversely proportional to the square root of the field strength and is given by:

                                                                             (1)

This is essentially the way a compass works. The compass needle is simply a bar magnet and its North-seeking pole is usually designated by a color or some other marking. The North-seeking pole of the needle always points North, because the Earth itself produces a magnetic field to which the compass needle responds. In fact, the Earth can be likened to a giant bar magnet, which is approximately aligned with its rotational axis. It is apparent that the way we distinguish between the poles of a bar magnet is to see to which magnetic pole of the Earth they point. Thus, the colored end of a compass needle and the end of a bar magnet marked "N" are properly called North-seeking poles because they point to the North magnetic pole of the Earth.

Current-Produced Magnetic Fields

About two hundred years ago, a novel way of producing magnetism was discovered by Oersted. When electric current is passed through a wire, a magnetic field is set up in the surrounding region. The strength of the field is directly proportional to the current. This effect can be optimized by winding the conductor into a coil of wire and making a large number of "turns" of wire in the coil. A special design, which is optimized to produce a region of uniform magnetic field, is called a Helmholtz Pair. The field produced when current flows through a Helmholtz Pair is constant throughout a region near the center of the coils. In this experiment, you will use the field produced by a Helmholtz Pair to calibrate an oscillating field sensor. The field sensor will then be used to measure the Earth’s magnetic field.