# Are two magnetic fields better than one?

I've recently attempted to find the best way to recover something that was lost in a [shallow] lake. While that may be unrelated from the question at hand (suggestions appreciated), I've been trying to figure out how to get the most out of my magnet purchase.

Say I purchase a single rare earth magnet (N&S poles labeled as being on the same side), with a 3" diameter and ~300lbs of pull. Then, I purchase 3 rare earth magnets, with a 1" diameter and ~100lbs of pull each. If I arranged the smaller magnets into a triangle pattern, would they produce a magnetic field similar to the single magnet? Would they only ever produce one third the force of the larger magnet? What if I connected them to a metal plate?

As I've tried to visualize magnet fields (with my small amount of knowledge on them), I keep imagining a larger magnet being better, even if it has a slightly less powerful field. Would a 10" magnet with a pull of ~100lbs act upon an object with about 10x the force at a given distance (in the center) than one of the smaller (1") magnets?

I've tried my best to research and find my answer to this question, but I must be terrible and searching because I can't find anything that even hints at what I'm looking for. I apologize for my naivete and greatly appreciate any answers I might receive!

What you are asking is called the superposition principle, that is, if I have two or more magnetic sources, what will the overall effect be?

Say I purchase a single rare earth magnet (N&S poles labeled as being on the same side), with a 3" diameter and ~300lbs of pull. Then, I purchase 3 rare earth magnets, with a 1" diameter and ~100lbs of pull each. If I arranged the smaller magnets into a triangle pattern, would they produce a magnetic field similar to the single magnet? Would they only ever produce one third the force of the larger magnet? What if I connected them to a metal plate

The total strength of the magnetic field depends on how you arrange them.

Take two two bar shaped magnets arranged in parallel. The magnetic north poles are at the bottom, the south poles accordingly at the top. Now look at the field lines, which indicate the strength of the magnetic field. The closer the field lines are together, the stronger the field.

Image Source: Fields of Two Magnets

Complicating things is the fact that this strong force can be attactive or repulsive, depending on how you line up the poles of the magnet.

Rather than try and arrange 3 or more magnets in a triangle, ( the shape you make with the magnets is not important), compared to getting the poles to line up in such a way that they do not cancel each other out.

As I've tried to visualize magnet fields (with my small amount of knowledge on them), I keep imagining a larger magnet being better, even if it has a slightly less powerful field. Would a 10" magnet with a pull of ~100lbs act upon an object with about 10x the force at a given distance (in the center) than one of the smaller (1") magnets?

If you buy a bar magnet, you can expect the strength to diminish by $r^{-3}$, where r is the distance away from the magnet. In other words there is a very rapid dropout of the strength of the magnet as you move it away from the object. So you will need to have your magnet relatively close to find it.

As far as I know, your best option is to buy 1 large magnet and work with that, trying to arrange more than one magnet will probably only reduce the overall field strength. Either that or buy more than one but keep them as far apart as practically possible (on a wooden frame?) to increase the chances of finding the object.