An Experiment on Magnetism

Written by Herb Rose on June 29, 2018. Posted in Current News

This is a simple experiment, inexpensive and easy to construct, to test if the force of a magnet decreases by approximately the cube of the distance from the magnet and the force between two magnets is equal to the product of the magnets divided by the square of the distance between them.

The procedure will be to determine the strength of two individual magnets and the measure the force between them.

The equipment needed consists of a block A frame (flat top) made from aluminum angle (1.5 inch). At the center of the top cross beam a 3/8 inch hole is drilled. In the middle of the lower cross beam a 1/8 inch slot is cut. The slot will be used to hang a 1/8 inch brass all thread rod by a brass nut and the top hole will be used to measure the distance to the top of the all thread rod by a depth micrometer.

The magnets to be tested will be the round disc composite magnets with a center hole. A brass i/8 inch nut is ground down and glued into the center hole of the magnets to provide a means of attaching them to the brass rod and an aluminum block for testing purposes. A steel washer, the same size as the magnet discs, is also fitted with a center brass nut.

A steel block weighing about two hundred grams and an aluminum block of similar weight are needed. The aluminum block has a counter sunk threaded hole in the center for using a brass screw to attach a magnet to it.

The measuring of the strength of the force from the magnet will be done by an electronic scale. The measurement will be in grams lifting power of the magnets and after the weight of the blocks is set to zero the strength of the magnets will be in negative grams.

The testing of the strength of the individual magnets was done by putting the steel block on the scale and tarring it to zero. The brass rod was hung by a brass nut on the aluminum frame and then its length was adjust to be as close to the steel block without registering on the scale. Using the depth micrometer the distance from the top cross beam to the top of the brass rod was measured. This is the zero distance used to determine the distance the magnet is from the block.

One of the magnets was then screwed flush to the end of the rod and the hanging nut was adjusted down to raise the magnet from the steel block. The distance to the top of the block is measured to determine the distance the magnet is from the block of steel and the force in negative grams is recorded for that distance. The brass nut is then adjusted up giving reading for the magnets strength at different distance until the magnet comes to close to the steel block and accurate readings can’t be measured. This procedure was then repeated on a second magnet to determine its strength.

The results of the two magnets were plotted on a graph giving the expected exponential curve with their strengths being nearly identical at about eighty five grams.

One of the magnets was then attached to the aluminum block by a screw coming through the underside of the block to be flush to the top of the magnet. The zero distance for the all thread was again determined and the second magnet was attached to the end of the all thread. The nut was adjusted down to raise the magnets and readings on the force between the magnets were recorded for various distance. The results were then graphed giving the expected exponential curve. What was not expected was that the force between the two magnets was about a hundred grams which was very close to the strength of the individual magnets. Something was obviously wrong.

The problem was that when measuring the strength of the individual magnets it was really measuring the force between two magnets. When the magnetic flux lines from the permanent magnet encounters the steel block it re-aligns the molecules in the steel releasing a magnetic force from the steel. The measurement for the individual magnets was really the measurement between two magnets, the constant force of the permanent magnet and the increasing force of the induced magnet.

That solved part of the problem but even if the strength of the individual magnets was half the measured force, the force between them was nowhere close to being the product of the two magnets. If it were it would lift the aluminum block off the scale.

The only other factor that could be in error is the distance between the magnets. The distance between magnets is measured from the center of one magnet to the center of the other magnet. This makes no sense since it would mean the force of the magnet is decreasing within the body of the magnet.

To test whether this way of measuring distance is right I designed a different magnet. On the brass rod I screwed one magnet up a distance and then screwed the steel washer up flus to the magnet. I then put the other magnet on the end of the rod leaving a cap between the top set of magnets and the bottom magnet.

I clamped the rod on the aluminum frame using another nut and moved the aluminum block with a permanent magnet attached and scale under the apparatus. This gave a reading on the force between the constructed magnet and the magnet on the aluminum block.

If the magnetic force of the constructed magnet is from the center of the magnet as the steel washer is screwed down, away from the top magnet and towards the bottom magnet the force recorded on the scale should be constant.

As the magnet descended the all thread the force recorded on the scale remained constant until the steel washer reached the midpoint between the top and bottom magnets. It then began to increase at an increasing rate as it descended.

This meant the constructed magnet was really three magnets. The top magnet was the permanent magnet and the induced magnet in the steel washer. The bottom magnet was the permanent magnet and the third magnet, which was the force registering on the scale, was a combination of the other magnets.

These results mean several things. As the steel washer was descending in the first half of the descent, the force of the combined magnet did not change on the scale and the strength of the top magnet was constant.  If this was the case then the strength of the induced magnet in the steel washer decreased as a function of the distance, not as the distance cubed.

This would explain why the force of a magnet appears to decrease approximately as the cube of the distance. As the permanent magnet gets closer to the steel block the strength of the induced magnetic increases and as it increases the distance to the permanent magnet decreases by more than the measured amount. There are two variables, magnetic strength and distance when measuring the strength of a magnet.

When the steel washer entered the magnetic field of the bottom permanent magnet it added to the force of that magnet increasing the force registered on the scale. Even though the magnetic force of the constructed magnet was the same when the washer was at the bottom magnet as when it was at the top magnet, the force between the aluminum block magnet and the constructed magnet increased. This would mean the force of magnets is additive and not a function of their products and the decline in the force of a magnet occurs when it leaves the magnet and should be measured from the surface of the magnet facing the object.

This gives us two equations for the force between magnets. The first is magnet1 times magnet2 divided by the distance between them squared, with the distance being measured from the center of two magnets. The second formula (assuming the two permanent magnets are equal) is magnet1 plus magnet2 divided by half the distance between their facing surfaces.

The distance between magnets is the distance from one magnet to the magnetic field of the other magnet. To determine the accuracy of the two formulas we use the results of the experiment to solve for the strength of the permanent magnet, which should be constant. The two equations, m=4F/d and m =Square root of F(d squared) both give similar results with  the strength of the magnet being fairly constant until the magnets get close together where its value drops. In the additive formula the value of m slowly increases.

If the two equations give the same answer the right one would be the one that best describes what is happening. If we have two magnets, surrounded by magnetic flux lines, as they approach each other the flus lines would combine to form a third magnet the force of which is being measured.

The closer the magnets became the more flux lines would combine increasing the strength of the combined magnet. This would cause the strength of the individual magnets declined and straighten the combined flux lines. This is exactly what the additive formula for force between magnets is describing while the traditional formula, where the force decline is by an area makes no sense. It also means the formula for the force of gravity between two masses is also incorrect.

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