# Determine how magnetic field varies with distance

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)

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## 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/d2 , where d is distance (or I = 1/r2 in the photo, where 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.

kelseymh2 years ago
You've missed an important point, which should be clear from the clip-art picture you copied into your Instructable! For a dipole, the field is not isotropic -- that is, it is not the same in every direction. Therefore, it is impossible for you to get a correct expression for the field as function only of distance -- such an expression assumes that 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 both distance from the center and as a function of the polar 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.
Bill WW (author)  kelseymh1 year ago
Thanks for reading and for the input.

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.
1 year ago
Ah, if you're measuring the force between two magnets, then it's really complicated, because the relative orientation of the two also has to be included. Good luck with your measurements!
Bill WW (author)  kelseymh1 year ago
I will defer to the gentleman with a Phd from CalTech. My lab instructor in physics (1963) was from Caltech.

Thanks much.

Bill
Olympia Wa
1 year ago
Wow. You must have taken Feynman's intro course! I was very sad (for many reasons), that my first visit to Caltech was in March 1988 (I started grad school there that September), a month after he passed away.

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 WW (author)  kelseymh1 year ago
It was an intersting experiment. Obviously what I did was not a properly conducted scientific experiment, but it furthered my education a bit.

Bill
1 year ago
Oh, I wouldn't say that! You had a hypothesis, tested it quantitatively, and falsified it. That's good science. Since you were making measurements which we already know about, I could give you additional information about your results (something we don't always get to do :-).
Bill WW (author)  kelseymh1 year ago
Thanks, but I may be going on to other challenges. Still haven't studied your double slit light Instructable, for instance.
rimar20002 years ago
Excellent work, Bill. My doubt is: are you sure that the poles of your magnet are symmetrically distributed? I ask this because it is possible to make magnets whit "abnormal" poles distribution.
Bill WW (author)  rimar20001 year ago
Thanks, Osvaldo.

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?

1 year ago
You asked, "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 best as 1/r3, because the lowest order is the dipole. Considering the distances to the nearest compact objects are hundreds of light years (9.5 trillion kilometers), even the strongest known fields (1010 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.
Bill WW (author)  kelseymh1 year ago