[geocentrism] magnetism and inverse sq.

I could not follow the math, algebra, but I gues they mean that dipoles upset 
the inverse square law .  Gravity does not have dipoles so everything is ok 
there.

Is inverse sq designated by a minus 2 which becomes minus 4 with a magnetic 
dipole..  Now does a -4 mean that with magnets the decrease in power much more 
rapidly by the power of 4 of the distance ..  If they had drawn the graph, I 
might have gotten it. 

Philip. 



The Force between Two Magnets as a Function of Distance



The force between two magnets is not necessarily inverse square. 


A digital scale can be used to measure the force between two magnets as a 
function of distance.
In this drawing the magnets are black. The upper magnet is glued to a meter 
stick.

Introduction

You can use a scale with a digital readout to measure the force between two 
magnets as a function of distance. A plot reveals that the force does not 
decrease as the inverse square of the distance.



Material

A scale to measure weight (with a digital readout.)

If your scale will read to +- 0.01 gram then:

two magnets, 1.25 inch diameter disk magnets from Radio Shack work well.

If your scale only reads to +- 0.1 gram then you will need to use neodymium 
magnets at least 2 cm x 2 cm x1 cm which exert larger forces on each other.

Graph paper and a calculator on which to take logs or log-log paper.

a hot melt glue gun.

A meter stick and a way to mount the meter stick over the pan of the scale, 
e.g. a ring stand with test tube clamps.

A metric ruler

Assembly

Tape one magnet on the pan of the scale. 

Zero the scale.

Hot-melt-glue the second magnet to the end of the meter stick, measurements 
will be easier if you glue it near the "0" end.

Mount the meter stick so that the magnet is exactly over the meter stick on the 
pan of the scale. Also mount the meter stick so that it can be easily slide 
up-and down, varying the distance between the two magnets. Create a reference 
point next to the meter stick that the distance the meter stick is moved can be 
measured.

To Do and Notice

Check that the scale reads zero when the upper magnet is removed. (Use the 
"Tare" option on the scale.)

Mount the magnet on the meter stick as far from the magnet on the scale as 
possible.

Note the reading on the scale, it should still be zero, or nearly zero.

Move the magnet on the meter stick closer to the magnet on the scale. The 
reading should increase if the magnets are set to repel. If the reading 
decreases remove the magnet from the scale and turn it over. Then start over 
again.

Move the magnet on the meter stick down until the reading on the scale 
increases.

Use the ruler to measure the distance between the centers of the two magnets. 
(This distance is equal to the distance between the tops of two identical 
magnets.)

Measure the force on the scale and record your data.

Continue to move the magnets together recording the force of their repulsion 
versus the distance between their centers. You should be able to devise a way 
of doing this with the meter stick to which one magnet is glued.

Continue measuring until the two magnets are almost touching.

Math Root Make a Graph

Plot a graph of force versus distance on regular graph paper.

Notice how the force changes with distance. The force gets weaker as the 
distance decreases.

Make a log-log plot of your data.  ????

Plot a graph of force versus distance on log-log paper, or plot the log of the 
force versus the log of the distance on regular graph paper.

Notice that over a range of distances the data lie on a straight line on the 
log-log plot. 

Measure the slope of the straight line. (Use a ruler to measure the rise versus 
the run.) The slope of the line will be near minus four. 

What's Going On?

On regular graph paper the graph of force versus distance is not a straight 
line. However on a log-log plot it is.

A straight line on a log-log plot is produced when the dependent variable is a 
power law of the dependent variable. i.e. when y = a xb.

The slope of the graph of y versus x on a log-log plot gives the power, b. 

If the line has a slope of 2 then y = x2. If the line has a slope of -2 then 
the force is y = x-2. If the force between the two magnets decreases as the 
inverse square then a log-log plot of force versus distance would be a straight 
line with a slope of -2. It is not. It is a line with a slope of -4.

If you could have magnetic monopoles, just a north pole or just a south pole, 
then the force between these monopoles would indeed decrease proportional to 
the inverse square of the distance. However magnetic monopoles have never been 
found in nature. Magnets always come with a pair of poles, north and south 
together called a magnetic dipole.

The force between two pairs of poles falls off proportional to the inverse 
fourth power of the distance between them. (The like poles repel and the unlike 
poles attract. The nearer poles exert stronger forces on each other than the 
more distant ones.)

So, at large distances, the force between these two magnets should fall off 
proportional to the inverse fourth power of distance. (Where large distance 
here means a distance large compared to the largest dimension of the magnet.)

These donut magnets are not tiny dipoles. When they get closer, each dipole on 
one magnet interacts with all the dipoles on the other, the dipoles range over 
many different distances at the same time. The resulting dependence of force on 
distance is complicated but when the distance between the magnets get small 
compared to the diameter the force becomes more constant with distance. The 
log-log plot rolls over and is no longer a straight line.

Other measurements

Measure the force between a magnet and a steel washer on the balance.

Notice that the dependence of force on distance is different. In particular the 
force drops off more quickly for the steel washer than it does for the magnet. 
The washer becomes magnetized when it is near a magnet. The magnetization of 
the washer falls off in proportion to the strength of the magnetic field from 
magnet. The magnetic field of the first magnet falls off as the inverse third 
power of distance, combined with the inverse fourth power fall off of the force 
between two magnets the resulting force falls off as the inverse seventh power. 
(However if the steel washer is not a perfect soft magnet, that is if it 
retains magnetization when removed from the presence of a magnet then the force 
will fall off somewhat more slowly than the inverse seventh power.)

Measure the forces between magnets with different shapes. Long rod shaped 
magnets have their north and south poles separated by a large distance. Over 
distances large compared to the diameter of these magnets and small compared to 
the length the force between two poles will be nearly inverse square.

Etc

The electric force between two spheres of charge decrease with distance 
inversely as the square of the distance. However When the charge is arranged in 
two long lines then the force falls off inversely proportional to distance (for 
distances small compared to the length of the lines.)

While if the charge is arranged in to sheets the force does not change with 
distance.

The same proportionalities hold for lights as well The intensity of a point of 
light decreases as the inverse square of distance, from a line of line 
inversely proportional to distance, and from a large flat plane of light the 
intensity does not decrease with distance.

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