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)

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.

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 <b>assumes</b> that the field is isotropic, which is not correct. <br> <br>Try holding your magnet in place, with the north pole pointing in some fixed direction. Now, measure the force as a function of <i>both</i> distance from the center and as a function of the <i>polar angle</i>, the angle between the north axis and the direction to your measurement point (on a globe, this is equivalent to the latitude). <br> <br>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.
Thanks for reading and for the input. <br> <br>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.
Ah, if you're measuring the force between <i>two</i> magnets, then it's really complicated, because the relative orientation of the two also has to be included. Good luck with your measurements!
I will defer to the gentleman with a Phd from CalTech. My lab instructor in physics (1963) was from Caltech. <br>I look forward to reading your Instructables. <br> <br>Thanks much. <br> <br>Bill <br>Olympia Wa
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. <br> <br>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.
It was an intersting experiment. Obviously what I did was not a properly conducted scientific experiment, but it furthered my education a bit. <br><br>Bill<br>
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 :-).
Thanks, but I may be going on to other challenges. Still haven't studied your double slit light Instructable, for instance.
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 &quot;abnormal&quot; poles distribution.
Thanks, Osvaldo. <br> <br>There are many variables, testing is not trivial. Yes, I have iron filings and will experiment. <br> <br>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? <br> <br>
You asked, &quot;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?&quot; <br> <br>No, such a field cannot be detected directly. All magnetic fields vary at <b>best</b> as 1/r<sup>3</sup>, because the lowest order is the dipole. Considering the distances to the nearest compact objects are hundreds of light years (9.5 <i>trillion</i> kilometers), even the <a href="http://en.wikipedia.org/wiki/Magnetar#Magnetic_field" rel="nofollow">strongest known fields</a> (10<sup>10</sup> tesla) are undectable. <br> <br>Magnetic fields of astronomical objects are measured spectroscopically. In a magnetic field, each spectral line is split into two slightly separated &quot;versions&quot; by the <a href="http://en.wikipedia.org/wiki/Zeeman_effect" rel="nofollow">Zeeman effect</a>. 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.
Thanks for your comments.<br><br>Looking forward to studying your double slit experiment.<br><br>Regards<br>Bill
1) I agree, the measures are not easy to do <br>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.
Maybe using iron filings you could visualize the poles of your magnet.

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Bio: I'm a retired mechanical engineer, woodworker, boater, and inventor.
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