Measuring the Strength of a Magnet

Measuring the Strength of a Magnet

Image: Rhett Allain. Three different magnets.

Measuring the Strength of a Magnet

Image: Rhett Allain. Three different magnets.

Bigger magnets aren't always "stronger". But how do you make a comparison between different magnets? One way is to determine the magnetic dipole moment of the magnet.

Magnetic Dipole Moment ———————-


Output from a VPython program



But how do you quantify this in some way? The key is to look at the magnitude of the field along an axis that runs through the two electric charges (or through the length of the bar magnet). In this case, it isn't too difficult to derive an approximate expression for the magnitude of the field. I won't do it here, but I do have a video version of this. Actually, that is the magnitude of the field along a perpendicular axis to the dipole - but you get the idea.


La te xi t 1

This result is only an approximation for the case that r (the distance from the center of the dipole to the location of the field) is much greater than s (the distance between the two charges in the dipole). I hope it's clear that q is the magnitude of one of the charges (the net charge of a dipole is zero).

But wait! How can we use and expression like this for a bar magnet? Magnets don't have two "magnetic charges" in them, do they? No, they don't. We can call the product of q and s the electric dipole moment. It would actually be a vector, but just don't worry about that for now. Using the same idea for a bar magnet, we can say that it has a magnetic dipole moment - μ. A bar magnet with a greater dipole moment will create greater magnetic fields.

Determining the Magnetic Dipole Moment ————————————–

Could you just measure the magnetic field at a certain location from a bar magnet and call it a day? Sure, but that wouldn't be much fun - would it? How do you measure the magnetic field anyway? Didn't I just go over that? Yes, I did but you weren't paying attention.


How do you find the magnetic dipole moment from that plot? You can't do it very easily. It's easier to deal with a plot that is linear. In that way, you can just add a linear fit and use the slope (and maybe the intercept). So, lets go back to the expression for the magnetic field due to a dipole.




  • Traditional Compass: μ = 0.2207 A*m2
  • iPhone Compass: μ = 0.0525 A*m2
  • xSensor: μ = 0.3077 A*m2

I was expecting some values that were a little closer in agreement. Perhaps it is clear that the iPhone compass doesn't give results that agree with the other two methods.

There is another magnet I was going to look at, but perhaps you can determine it's dipole moment as a take home lab assignment. Here's the magnet.

I Photo


I Photo 2

Yes. The box says "cow magnets". They happen to work fairly well for experiments that require a bar magnet. What is a cow magnet? Apparently cows eat stuff on the ground. Usually this "stuff" is grass. However, sometimes this "stuff" that goes into the cow is non-grass objects like old staples and nails. If these staples and nails get into the smaller parts of a cow's stomach, it can cause damage. The cow magnet is then placed in the cow to attract these iron objects and prevent them from getting into the small stomach parts. I tell students that I got these magnets on the cheap end because they were already used.
