# Calculating the force that a permanent magnet exerts on a particle

• MMImpel
In summary, the conversation is about the force generated by permanent magnets on particles and the different setups that can be used to attract the particles. The question asks for advice on which equations to use and how to compare the force generated by different setups. The conversation also includes discussions on the use of stainless steel and the types of particles being manipulated. The experts suggest using simulations or experiments to find the best solution.
MMImpel
TL;DR Summary
Is it possible to make rough calculations to calculate the force that a parmanent magnet exert on a small particle?

I have a question regarding permanent magnets and the force they generate on particles, which is far from my comfort zone. I have the option on using two types of permanent magnets and with two different setups. Imagine that we want to attract small particles using the magnets. Assume that the same particle is placed on the same distance from both magnets, let's say 10 mm.

1. A magnet with 12 000 Gauss with given dimensions put directly in the vicinity of the particles
2. A magnet with 12 000 Gauss with given dimensions (the magnet is smaller in size compared to 1), but around the magnet there is a thin air pocket (lets say 0.1mm around the magnet) and then also a casing of stainless steel of 0.1mm.
Coming from the field of heat transfer I am used to work using the electrical analogy, where can get a heat transfer resistance by taking each material dimension and heat conductivity into account to find the total heat transfer rate. I understand that magnets generates a magnetic field, and when I have tried to search for this I have mostly found FEM tools.

I would like to get a rough estimate to compare, i.e. is the force 2 or 3 times higher? Any advice on how I can reason or what equations I can look into?

You didn't define vicinity, nor if you will be using a permanent magnet... that makes the question rather ill-defined.

However...
Most Stainless Steels (SS) are non-magnetic, so they would act only a a spacer... just as an air gap would.

Some SS are magnetic. If using one of those, then treat it as any other pole piece using the appropriate magnetic properties, shape, and dimensions. If the casing completely encloses the magnet then the external field will be reduced, see the previous sentence.

Cheers,
Tom

DaveE and hutchphd
Dear Tom.G,

I am sorry for the confusion. Both magnets are permanent magnet with 12 000 Gauss. The SS are not magnetic. I have attached a sketch to make the problem more easy to understand.

Any advice regarding which equations I should look into or any example? I have never worked with magnets and these types of calculations before so I am quite lost

Sorry I can't be of much more help, it has been decades since I have even mildly dealt with this subject.

A Google search turned up many responses, some of which, of course, were useless:

I have sent a request for help by other advisors here, that should get you more and better responses.

Cheers,
Tom

p.s. Your drawing shows a particle half way between the poles of a bar magnet. The net force at that position is approx. Zero, equal force toward both poles. You would get better results if the particle is on the magnetic axis of the magnet.

It's complicated and there won't be a good solution without spending a lot of time on a simulation - simply testing it will be much easier. It will depend on details of the magnet, and it will depend on the type of steel as well.
Tom.G said:
p.s. Your drawing shows a particle half way between the poles of a bar magnet. The net force at that position is approx. Zero, equal force toward both poles. You would get better results if the particle is on the magnetic axis of the magnet.
There should be a force towards the magnet if the magnet is too long (don't see the length given). It's likely to be stronger without the steel as that will act as flux return.

DaveE
Perhaps you could be a bit more specific as to the purpose here. I have done some work in designng small magnets to manipulate magnetic particles.
The stainless may or may not change the field. You need to characterize the particular steel either by published specification or by simple experiment. It may make a large difference if ferromagnetic
The force on a ferromagnetic particle will depend upon the gradient of the field. The field for a long thin magnet can be modeled as monopoles on a stick.
I have also used a program called vizimag which was freewear two decades ago. It was really useful and simple. It may not exist now. Happily this looks like essentially a 2D problem.

Charles Link and DaveE
MMImpel said:
I have a question regarding permanent magnets and the force they generate on particles

hutchphd said:
The force on a ferromagnetic particle will depend upon the gradient of the field.

@MMImpel -- I don't think you said that your particles are ferrous. Are they? What are they composed of? If they are not ferrous, why are you wanting to manipulate them with magnetic fields?

mfb said:
It's complicated and there won't be a good solution without spending a lot of time on a simulation - simply testing it will be much easier. It will depend on details of the magnet, and it will depend on the type of steel as well.
There should be a force towards the magnet if the magnet is too long (don't see the length given). It's likely to be stronger without the steel as that will act as flux return.

I would just love to have some estimates, otherwise I will ofcourse do a practical test to determine the distance.

Rod 1) is 42 mm high with a diameter of 9 mm.
Rod 2) is 30 mm high with a diameter of 7 mm.

Excatly, I noted that the steel seems to make the magnet much weaker, but the volume of the rods are also quite different so that is also a reason for my questions, how much is it due to the dimensions if the rod and due to the stainless steel (304).

hutchphd said:
Perhaps you could be a bit more specific as to the purpose here. I have done some work in designng small magnets to manipulate magnetic particles.
The stainless may or may not change the field. You need to characterize the particular steel either by published specification or by simple experiment. It may make a large difference if ferromagnetic
The force on a ferromagnetic particle will depend upon the gradient of the field. The field for a long thin magnet can be modeled as monopoles on a stick.
I have also used a program called vizimag which was freewear two decades ago. It was really useful and simple. It may not exist now. Happily this looks like essentially a 2D problem.
The purpose is to see if we can attract, for instance, magnetite particles flowing in a water tube. The steel around the second rod is of type SAE-304.
berkeman said:
@MMImpel -- I don't think you said that your particles are ferrous. Are they? What are they composed of? If they are not ferrous, why are you wanting to manipulate them with magnetic fields?
They are, what I would want to do is to get them to stick to the rod. Let's say you have a tube system filled with a mixture of water and some ferrous particles, so I want to see if this "filter" would be able to help me collect the particles from the water stream.

If you wish to maximize the "pull" over a short distance then a configuration using both poles (like a" horseshoe magnet") is much stronger.
The magnetic properties of stainless steel are quite variable depending upon heat treatment and even mechanical working so be aware that this is likely to be a problem.
Are you looking to filter the stream or simply sample it for the presence of particles? Why the "wand" shape?

mfb
hutchphd said:
If you wish to maximize the "pull" over a short distance then a configuration using both poles (like a" horseshoe magnet") is much stronger.
The magnetic properties of stainless steel are quite variable depending upon heat treatment and even mechanical working so be aware that this is likely to be a problem.
Are you looking to filter the stream or simply sample it for the presence of particles? Why the "wand" shape?
Thank you for the advice, I will think about that type of geometry.

The reason for the "wand" shape is because we need to insert the rod into a tube, thus making the "hole" as little as possible. I am looking to filter the stream, like insert the rod for a couple of days and then take it out of the stream with the particles attatched to it.

So if the size is different but both have the same number of Gauss, can we draw some conclusions just from that?

Why do you need to "insert" anything? What is the tube ? Will the field penetrate through it?
The issue is not just the field strength. The gradient supplies the motive force to the particles, so everything about the shape matters. How much resource can you throw at this effort and how critical is the result? What is the venue here?

If both magnets have the same geometric shape, but the difference is just is size?
It seems like this question is too hard to get an rough estimate for, maybe just buying a bunch of magnets and testing is the best way.

I, for one, am really confused as to what you are trying to do. It seems like you want to remove suspended particles from a water stream, and the requirements you have been given are vague. Example: like you have a milling process and you want to recycle coolant.

So. Buying lots of magnets and testing sounds like a great idea. If you want to remove all particles then try a flange filter set up. -- assuming to have water flow through a tube.

mfb
This thread is an example of an x-y-question: You have a problem that you don't know to solve. Instead of asking about that problem you come up with a setup that you think will work, but you don't know how to do that either. You start a thread asking questions about that setup instead of asking about the original problem. No one can help for three reasons:
- you didn't provide enough information about the system you think of
- the quantity you asked about is not the relevant metric for your original problem
- and the setup you think of looks like a poor choice for your original problem

If you want this thread to be productive, start with a description of your original problem. What do you want to do?

Tom.G, berkeman and hutchphd

## 1. How do you calculate the force that a permanent magnet exerts on a particle?

The force that a permanent magnet exerts on a particle can be calculated using the formula F = (magnetic field strength) x (particle's magnetic moment) x (sin θ), where θ is the angle between the direction of the magnetic field and the direction of the particle's magnetic moment.

## 2. What is the unit of measurement for the force exerted by a permanent magnet on a particle?

The unit of measurement for the force exerted by a permanent magnet on a particle is Newtons (N).

## 3. How does the distance between the magnet and the particle affect the force exerted?

The force exerted by a permanent magnet on a particle is inversely proportional to the square of the distance between them. This means that as the distance increases, the force decreases.

## 4. Can the force exerted by a permanent magnet on a particle be negative?

Yes, the force exerted by a permanent magnet on a particle can be negative if the particle's magnetic moment is in the opposite direction of the magnetic field. In this case, the force will be attractive rather than repulsive.

## 5. How does the strength of the magnet affect the force exerted on a particle?

The strength of the magnet, or the magnetic field strength, directly affects the force exerted on a particle. A stronger magnet will exert a greater force on a particle compared to a weaker magnet, assuming all other factors remain constant.

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