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# Physics/Stacking magnets

Question

Magnet stack
QUESTION: Hello Steve,

I have been researching magnets, and in particular, stacking magnets on top of each other. I found a website that said "two or more magnets stacked together will behave exactly like a single magnet of the combined size." ( http://www.kjmagnetics.com/FAQ.asp#stack ) I am wondering if you can help me understand how the magnetic field would behave if I stack an electromagnet on top of a permanent magnet.
In the attached image, an electromagnet is positioned on top of a permanent magnet. I am wondering how I could calculate the magnetic field strength when the electromagnet is off and also when the electromagnet is turned on. For example, if the permanent magnet has a field of 100 Gauss, when the electromagnet is off, I am guessing the field strength at Point A is 100 Gauss, and the field strength at Point B is 100 Gauss minus the loss due to the 1mm distance between points A and B. Would this be essentially correct?
What about when the electromagnet is turned on? If the permanent magnet has a field of 100 Gauss and the electromagnet has a field of 100 Gauss, will the magnetic field at Point B simply be 200 Gauss, or would the permanent magnet's field still decrease with the distance from Point A to Point B to the same extent as when the electromagnet is switched off?
Based on the fact that two stacked permanent magnets are reported
to have a combined magnetic field equivalent to the sum of the two individual magnet's fields, it seems like an electromagnet stacked on a permanent magnet will also have a combined strength equivalent to the sum of the two fields - in this case 200 Gauss. Have I reasoned this correctly?
Some people I have spoken to are confident that the permanent magnet's field will still experience a loss due to the distance between Point A and B and there for the combined strength of the electro and permanent magnet will actually be much weaker. I have noticed that a magnet that attracts a nail will cause that nail to then attract a second nail. The second nail is too far away to be attracted by the magnet alone, but the presence of first nail somehow extends/strengthens the magnetic field and negates the decrease in field strength due to distance to allow the second nail to be attracted. Does this phenomenon mean that my stack of electromagnet and permanent magnet will simply have a field strength of 200 Gauss, or will the permanent magnet's field still drop off with distance?

Sorry for the long and involved way of putting the question. I probably could have made the question much shorter, but I find it hard to explain exactly what is in my head!

Thanks again and best regards,
Eddie

Again I have to caution you that I can't say that I have expertise in these topics. I am going to say "it depends". If your electromagnet has an iron core (or a core of some magnetic material) I think that, with the electromagnet turned off, at point B you will have close to 100 Gauss. My thinking is that the core will act much like the first nail that you put in contact with the permanent magnet. And with the electromagnet turned on, that you will have close to 200 Gauss.

If your electromagnet has a hollow core on the other hand, I would expect the permanent magnet's field to decrease with the distance from Point A to Point B to the same extent as when the electromagnet is not in the vicinity. With the electromagnet in place as shown in your figure, that decrease of the permanent magnet's field with the distance from Point A to Point B would be the same with the electromagnet switched on or off. The field at point B would increase by 100 Gauss when you turn the electromagnet on.

Again, these are my expectations. My confidence is not 100%. I think this is an effect that you could test.

I hope this helps,
Steve

---------- FOLLOW-UP ----------

Magnet stack configura
QUESTION: Hi Steve,

I would just like to ask a follow up question to an answer you gave me in mid December.
I had asked you a question about stacking an electromagnet on top of a permanent magnet, and how the two fields might interact and/or combine.
I am getting ready to do some tests, but a thought has been bouncing around in my mind and I was wondering if you could me your opinion on this.
I was curious about what would happen to the magnetic field of a permanent magnet when an electromagnet was placed on top of it.
You told me that -
"If your electromagnet has an iron core .. I think that, with the electromagnet turned off, at point B (at the top of the electro mag+permanent mag stack) you will have close to 100 Gauss. My thinking is that the core will act much like the first nail that you put in contact with the permanent magnet. And with the electromagnet turned on, that you will have close to 200 Gauss."
If your electromagnet has a hollow core on the other hand, I would expect the permanent magnet's field to decrease with the distance from Point A to Point B to the same extent as when the electromagnet is not in the vicinity."
I am now wondering how the magnetic fields might behave if the electromagnet's core was actually part iron and part air, or in fact part iron and part plastic. I have attached an image with some basic designs of the type of thing I mean. As you can see, there is a plastic section between the permanent magnet and the electromagnet. Number 2 has a copper coil which is wrapped around both the soft iron core of the electromagnet above, and the permanent magnet below. Number 3 has soft iron strands connecting the electromagnet and the permanent magnet, but the connection between the two is mostly plastic.
What might conceivably happen in these scenarios to the field of the permanent magnet? If the permanent magnet's field at point B is reduced by the presence of the plastic section, how might the field behave when the electromagnet is switched on? Could turning on the electromagnet cause the permanent magnet's field to be any stronger at point B?
Would the only difference in magnetic field strength of the combined magnets at point B between when the electromagnet is switched off and when it is switched on, be the strength of the electromagnet?
Sorry to pepper you with some many questions. Like I say, we are getting ready to test this, but it would be really, really useful to hear you thoughts.

Once again, thank you and best regards,

Eddie

Hi Eddie,

http://en.wikipedia.org/wiki/Electromagnet

I want to talk about the difference between the drawing of an air core solenoid (just above the section heading "How the iron core works" and the drawing of an electromagnet with iron core in the section with the heading "Magnetic circuit – the constant B field approximation".

Notice in both that the lines indicating magnetic field have arrow heads. They show that in general the magnetic field emerges from one end of the coil and return to the other end of the coil. The lines used in the drawings are not literal but are good aids to understanding. Notice that each line loops around to its beginning. I said "in general" above because I want to point out that there are some exceptions to my saying the "field emerges from one end of the coil and return to the other end of the coil". This is true in both drawings but more clear in the second one --> some of the lines take short cuts in returning to the other end. That's much more true when there is no core. Unless there is a magnetic circuit (such as an iron core) the magnetic field line is much more likely to curve and return as soon as possible to the other end of the line.

If your core is less than completely iron or other suitable magnetic material, it will be less effective. There will be more leakage (see the discussion about leakage flux). I assume that in all 3 of the designs of your drawing that the core is part iron and part plastic. I have assigned numbers 1-4 to your questions.

1.
Design 1: More of the field will leak out of the desired path and return to the bottom end of the permanent magnet that if the core were solid iron.
Design 2: Same as for Design 1.
Design 3: This will be slightly better than Design 1. (Notice the 4 conditions listed just below the second of the Wikipedia drawings I referred you to.)

2. I do not expect that the pattern of the permanent magnet's field lines will change with the electromagnet turned on.

3. I do not expect that it will.

4. I think yes.

Notice that I am not certain of my answers. I hope this helps you some.
Steve

Physics

Volunteer

#### Steve Johnson

##### Expertise

I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.

##### Experience

I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

Education/Credentials
BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University