Measure the magnetic force of a chain of spherical magnets and you’ll discover that it’s not how many magnets you have, but how they’re arranged, that makes all the difference.
- Small ceramic disk or ring magnet
- Transparent tape
- Digital scale that measures to the 0.1 grams or smaller
- Ten small rare-earth magnetic spheres (the 5-mm size works well)
- Clear plastic container large enough to just fit over the scale
- Several drink coasters, small paper notepads, or similar (blocks of Post-It notes work well) to raise the height of the scale
- Optional: more rare-earth magnetic spheres for additional experimentation
- Tape the disk magnet to the weighing plate of the scale (see photo below). Then tare (zero) the scale.
- Place the plastic container over the scale, so it acts as a clear cover. Use coasters or pads of paper to raise the height of the scale so the magnet is approximately 1/2 inch (1 cm) below the cover.
- Looking straight down on the scale, mark the plastic container to note the spot directly above the magnet (see photo below).
Take 10 rare-earth magnetic spheres and assemble them into a chain. Then, holding the chain vertically over the disk magnet, slowly bring it toward the scale. (You’ll probably need two hands to hold the chain straight, as it will try to veer away.)
> Notice that, if you hold the chain one way, it’s attracted to the disk magnet (click to enlarge the photo and diagram below). If you flip the chain over and hold it the other way, it’s repelled. Since most scales won’t properly measure negative values, you’ll get better measurements if you hold the chain of magnets so they repel the magnet on the scale. (If your digital scale is okay with negative values, though, you can use the stack either side up.)
Hold the chain vertically over the scale and watch the reading as you slowly move the chain closer to the magnet, and then farther away. You’ll see that the reading varies with distance. Because of this variation, you’ll want to have each chain the same distance over the scale as you work, so you can make comparisons with other arrangements.
For consistency, place the chain so that it just touches the marked spot on the plastic container. Hold the chain in place, and record the reading on the scale (see photo below).
Pull the chain apart so it’s only half as many spheres (5, rather than 10). Set this short chain in place above the magnet, as you did before, and record the reading on the scale. Surprised? The new reading isn’t half the original reading. Play with the length of the chain. What do you notice?
Rebuild the chain so that it’s 10 spheres long again. Then fold the chain in half. (It might spontaneously become a circle; if so, just squash the chain flat so it forms a double line 5 spheres long and 2 spheres wide. Click to enlarge the photos and diagram below.)
Bring this new chain near the scale and record the reading, as shown in the diagram below. Are you surprised by the result?
Let’s try something that’s similar but not quite the same. Make the 10-sphere chain again, and then split it into two 5-sphere chains (see diagram below).
Bring the a-e chain towards the f-j chain so that sphere a is near sphere f. As the chains get closer, you’ll see them bend away from each other, as shown in the diagrams below.
Keep bringing the chains together. Once the two chains are close enough, you’ll be able to see them snap into place, with one chain offset from the other chain, as shown in the diagram below.
Bring this pair of chains near the scale and record the reading (see diagram below). How does it compare to the reading for the folded-over chain? How are these two chains different?
Each rare-earth magnetic sphere is a magnet with a north and south magnetic pole. When you let them form a chain, they align so the north pole of one sphere touches the south pole of the next. In the diagram below, the arrows point towards the north pole of the small, spherical magnets as well as the larger magnet on the scale.
While each additional sphere increased the total strength of the chain of magnets, you may have been surprised to find that a chain twice as long was not twice as strong.
The magnetic force between two magnets is highly sensitive to the distance between them. As a result, the addition of extra spheres at the far end of the chain makes less of an impact than you might expect: A 5-sphere chain results in a measured force only slightly less than a 10-sphere chain.
When you fold the chain, each sphere is paired with a sphere whose poles point in the opposite direction. Each sphere’s force is canceled out by the one next to it (see diagram below), and the overall force on the scale drops to near zero.
When you allow the magnets to form in staggered rows, their poles can add together instead of canceling, making a stronger overall force (see diagram below).
If you have extra magnetic spheres, try attaching additional strands in the staggered fashion. You’ll notice that the force will increase with each strand. You’ll also notice that the spheres will start to splay away from each other, making it difficult to keep the strands together. This is why extremely strong magnets are often also very fragile: Repulsive forces within them make them ready to tear themselves apart.
Students can start with one sphere and measure the force, add another sphere and measure the force again, and continue measuring sphere by sphere. Once they have that set of information, they can graph the scale readings for up to 10 spheres. They’ll notice that, at first, each sphere will seem to increase the force by the same amount, but at some point, the trend will change, and the effect will get smaller with each additional sphere.