Illuminating a dipole field

Demonstration goals:

Show a dipole field

Show the "lines of force" which extend from one pole of a magnet to the other

Q:If you stood at the North pole, which way would your compass point?
A:To the Southwest!

Surprisingly, the Earth's North Magnetic Pole is not located at its North Geographic Pole; instead, it is at 78.5N, 103.4W (shown by the star in the image). This odd state of affairs comes about because of the nature of the Earth's magentic field...

Definition: A dipole field is any field of force that is created by two poles separated in space, such as any electrical or magnetic field. The resultant force from a dipolar field varies as r^-3, instead of r^-2. A dipolar magnetic field can be generated by a magnet or by an electrical current; it was this realization that lead James Clerk Maxwell to the equations which unified the electrical and magnetic forces into the electromagnetic force.

One of the most common ores of iron is magnetite, also known as lodestone. Since lodestone has distinct north- and south-seeking poles, it has been used since at least 500 BCE as a method of finding the North Pole. Peregrinus of Maricourt wrote the first surviving treatise about the properties of magnets. (Some Chinese writings pre-date his work, but they do not describe the magnet itself, only "south-pointing wagons" and "south-pointing stones"). His basic observations are still valid today:

Magnets have two poles: one north-seeking and one south-seeking
Like poles repel; opposite poles attract.

Today, we would add that the "lines of force" that connect the two poles emerge from the north-seeking pole and enter at the south-seeking pole, and that the magnetic field is strongest where these lines are closest together. It is important to note that the lines of force are a convenience only, and do not actually exist! They simply make it easier to visualize what the field of forces is doing at a given point.

In the early 1600's, Sir William Gilbert suggested that the Earth has a magnetic field shaped like the one around a magnet. He also believed (incorrectly) that the planets were held in their orbits by magnetism. Since Gilbert's time, we have also learned that the Earth's magnetic field moves with respect to its rotation axis. This drift is called secular variation. It is possible that this is caused by the inner core rotating at a different speed than the mantle; an alternative theory is that there is a standing wave in the outer core which moves with respect to the mantle, creating the secular variation.

We have also learned that there have been reversals in the Earth's magnetic field; these are recorded in the seafloor magnetic anomalies. In 1963, Vine and Matthews interpreted these stripe-shaped patterns as evidence for sea-floor spreading and laid the foundation for plate tectonics.

While we won't be creating any new seafloor (we do that in our simple Euler pole demonstration), we will be demonstration the basic nature of a dipole field such as the Earth's. To perform this demonstration, you will need:

Magnetic Field Box (Fisher CHS430591 $94.30 or Wards 80H0003 $115.00)
Alternatively, you can make a field box with:

Glycerine

Zip-Lock_(tm) bag (The kind that makes a water-tight seal)

Steel wool or fine iron filings
In either case, you will also need:

Small magnet (One come with the kit)

Small nail suitable for placing into the field box's aperture (5 cm long by .3 cm dia {2 in x .2 in})

Fine copper wire (about 2 m {6 ft})

Toy train transformer

Tape

Table or other flat, hard surface

Before the demonstration: Measure off about 15 cm of wire, and make a bend in it. Tape the wire to the nail so that the measured section runs from the point to the head. Begin winding the wire around the nail at the head, spacing the turns as closely as you can. When you come to the point, place a layer of tape around the wire, run the wire back to the head and start winding again. Repeat so that there are three layers of wire on the nail. Place a last layer of tape over the wire, and trim the ends of the wire so that they are approximately equal in length. Strip the wire for use.
To assemble the field bag, shred the steel wool into very fine pieces. Place them into the Zip-Lock_(tm) bag. Pour in enough glycerine to half-fill the bag. Zip it closed. For extra security, you may want to tape over the opening as well.
If you are using an overhead projector, make certain that it is working before the class. Connect the wires from the nail to the toy train transformer and make certain that it is ready for use.

1. Shake up the field box/bag and place it on the table or projector stage. Note that the iron filings are distributed randomly and have no preferred orientation.

2. Now insert the magnet into the field box (or place it on top of the field bag. Watch as the filings begin to line up and draw closer together. The places where the filings congregate are roughly equivalent to the "lines of force" which extend from one end of a magnet to the other.

3. Reverse the magnet and watch what happens.

Now let's explore the effects of electricity.

4. Make certain that the transformer is turned off. Replace the magnet with the wire nail. Note that nothing happens. Turn on the transformer and watch as the filings line up again.

5. Reverse the current (by swapping the wires) and compare the results.

For Discussion:
How do the fields of the magnet and the electromagnet compare? Why do you think the differences exist?