This Instructabler describes how to make a scientific investigation to determine how magnetic field varies with distance. Two methods are presented , and reasonable conclusions made.

Note that the magnet used in this Instructable is a thin disk type, not a bar magnet.

Tools and equipment:

One rare earth neodymium magnet, 16mm diameter x 3mm.

Precise scale measuring to 0.1 gram

Balance beam apparatus to allow measuring magnetic attraction

Magnetic compass

Tape measure (non magnetic)

**Signing Up**

## Step 1: Some background: inverse square law?

Many phenomena of nature, like light, obey the inverse square law. That means as you get farther away from the source of light, the intensity decreases as the square of the distance. The inverse square law applies to light, gravity, and electrostatic charge. And the equation is simple and beautiful: basically it is ** I = 1/d ^{2}** , where d is distance (or

**I = 1/r**in the photo, where

^{2 }**r**is distance) and

**I**is intensity.

It is often assumed that the strength of a magnetic field also obeys the inverse square law. Researching the Internet produces many complex equations, most indicating that magnet field varies inversely with the third power of distance, in other words an inverse cube law.

Since it all seemed vague, or at best theoretical, I decided to test for myself.

## Step 2: First trial: Measure magnetic attraction using precise scale

My initial plan was to build a device that could measure magnetic force at various distances using a precise scale. I then would analyze the data, plot a graph, and come up with an equation. It turned out to be not that easy. The device is shown in the photo:

- The magnet is attached at the end of a threaded brass rod, 16 threads per inch.
- The magnet is attracted to the cast steel surface of my table saw.
- All components are non-magnetic, brass, aluminum, wood.
- Force is measured by the scale at 1/16" intervals over the full range the magnet is attracted to the steel, and recorded in a table.

assumesthat the field is isotropic, which is not correct.Try holding your magnet in place, with the north pole pointing in some fixed direction. Now, measure the force as a function of

bothdistance from the center and as a function of thepolar angle, the angle between the north axis and the direction to your measurement point (on a globe, this is equivalent to the latitude).If you plot the data as a function of polar angle at a fixed distance, then you should see an interesting relationship. Conversely, if you plot your data as a function of distance at a fixed polar angle, you should see another interesting relationship.

Yes, there are a lot of issues that make magnetic field not trivial. Interesting point, to use polar angle and latitude, will try it. I found that results varied greatly with small changes in the angle the magnet is held.

twomagnets, then it's really complicated, because the relative orientation of the two also has to be included. Good luck with your measurements!I look forward to reading your Instructables.

Thanks much.

Bill

Olympia Wa

I still think this is an awesome instructable idea, and you've written it up quite well! I had forgotten that you were using a compass needle as the probe. Since this spins freely on it's axis, you can actually use it to trace out the orientation of the field lines around your test magnet, and take care of the polar angle dependence that way.

Bill

There are many variables, testing is not trivial. Yes, I have iron filings and will experiment.

This is interesting to consider: One of the most powerful natural magnetic fields is from a neutron star. Can this field be detected on earth, and would that field vary as inverse square?

No, such a field cannot be detected directly. All magnetic fields vary at

bestas 1/r^{3}, because the lowest order is the dipole. Considering the distances to the nearest compact objects are hundreds of light years (9.5trillionkilometers), even the strongest known fields (10^{10}tesla) are undectable.Magnetic fields of astronomical objects are measured spectroscopically. In a magnetic field, each spectral line is split into two slightly separated "versions" by the Zeeman effect. The spin-up and spin-down electrons in a given atomic energy level have slightly different energies (and hence spectral frequencies) depending on whether they align with or against the local magnetic field. The magnitude of this splitting is proportional to the local field strength.

Looking forward to studying your double slit experiment.

Regards

Bill

2) Surely very sensitive instruments could detect these magnetic fields. But measure its variations with distance, it is another question. I don't think that be possible.