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# electromagnetic field measurement

## electromagnetic field measurement

(OP)
Hi guys, I'm new to this forum and I have what I think is a basic question.  I'm not much of an electrical engineer, so I hope it does not sound too silly.  I have the basic equations that characterize the magnetic field on axis with a solenoid shell at a distance away from the solenoid.  However since the field falls away so quickly I wanted to concentrate the flux with a solenoid with some sort of core (probably ferrite).  I only need a magnetic field a few millimeters away from the electromagnet, but it will not make contact with the magnetic substrate.  I have tried to find equations to help characterize the field away from a solenoid with a core but have not been able to.  I also looked for commercial electromagnets that may have specific field equations for that particular electromagnet, but none I found have the formula, plus they are all contact electromagnets.

Any ideas on where I can get (or I guess make?) an electromagnet to attract a magnetic material from a distance of a few mm and its magnetic field equation so I can model it?

I'm currently working on specifics, as to how much of a field will be necessary to create the force I need.

George

### RE: electromagnetic field measurement

Hello George.

This type of question comes up quite frequently on this forum, for example see threads:
237-84957
340-132216
(to find these, cut and paste the number into the search box at the top centre of the page, and go to the list box "Find a Forum" and select "Thread Number").

I agree the best way to increase the flux density (and therefore the force) is to place a core within the solenoid, but that is when the analysis becomes more complex.  Flux lines ALWAYS form a closed circuit (passing through the solenoid) so ideally you need to close this circuit as far as possible with the core, so that the airgap (in the direction of the flux) is the smallest practical length.

If your airgap is large then the magnetic reluctance* of your magnetic circuit will be large (i.e. for a given number of ampere turns, the flux density will be reduced), and also the flux in the airgap will fringe (i.e. "bulge" outwards, for want of a better word, and not go where you want it to go) making it more difficult to analyse.  Unless the airgap is small enough to keep the flux lines linear, you will most likely need to either determine the field by experimentation/measurement, or by using finite element analysis.

Is a short airgap feasible with your device?

* if you are happy with an electrical circuit analogies,  for a magnetic system:
ampere-turns  ->   voltage
flux          ->   current
reluctance    ->   resistance

### RE: electromagnetic field measurement

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### RE: electromagnetic field measurement

(OP)
Fantastic, thank you for your help.  I see you are steering me toward a "C" shaped electromagnet.  I was originally (and maybe naively) thinking/hoping to be able to use a cylindrical type electromagnet to create the actuation.  You think that is not the way to go?

George

### RE: electromagnetic field measurement

Absolutely, if you close the magnetic path as much as possible with a core to guide and concentrate the flux you will get a dramatic increase in force.  If you look at holding magnets and lifting magnets, that is exactly what they do - the steel workpiece bridges the poles and closes the magnetic circuit.

There are a some issues to consider:
1. the core must be of adequate cross section so that it doesn't magnetically saturate, this would result in an increased reluctance and reduce the total flux.  A reasonably simple calculation can calculate approximately the required minimum cross section to prevent saturation.
2. after the current is switched off there is always some residual magnetism in the core and this can be enough to continue to hold the workpiece (or whatever) although if there is a small airgap (or non-magnetic spacer) this will not be a problem.
3. the attractive force is proportional to flux density  B2, and as the airgap is closed B increases quickly in a non-linear fashion, so the overall force is certainly not linear with airgap length, or with coil current.
4. there are different ways to look at the calculation: you can start with the required force and calculate the required  number of turns, current and core area; or you can calculate the force from a given coil and current.  Either way, you will need to specify the material magnetic properties and especially the length of any airgap.

### RE: electromagnetic field measurement

(OP)
This has been a great help...I guess there is one more thing then I am confused about.  I did read through those other threads.  I think i can keep the gap to under 1cm

So, if I understand correctly, the flux within the airgap (if it is relatively small) is fairly constant.  What then is the attractive force equation for a location in the airgap between the two faces of the electromaget?

I was under the impression that the force due to a magnetic field on an object in that field is actually a result of the difference of the field across the length of the object.  Now with what we assume to be a fairly constant field (if I undertand correctly) how do you calculate the force on an object in that field?

Thanks again,
George

### RE: electromagnetic field measurement

Hello George

The equation for the attractive force between two pole faces is derived from the equation for energy stored in the field in air.
Force (in Newtons) F = B2*A/(2*μ0)
where B is the flux density in the airgap (Tesla)
A = area of pole face (or area of airgap in direction perpendicular to flux) (m2)
μ0 = permeability of free space (=4*pi*10-7)
i.e. all in SI units

Regarding your comment about the force being "as a result of the difference of the field across the length of the object", I have a problem with your use of the word "field" because a field is a concept, not a parameter as such.  If you mean the magnetizing force (H) appearing across the airgap then yes I agree, and the force is proportional to H2 because B is proportional to H.  In fact B=μ0H in the airgap.  Better to stick with the equation given at the top, it's less confusing I think.  The basic concept of magnetic fields is easy, it's the way we model it mathematically (in order to describe what happens) that takes a bit of getting used to.

Your airgap of 10mm is ok if the pole face area is relatively large - if I had to put a figure on it, at least say 10 to 20mm in diameter (assuming a round pole).  It is normal to approximately calculate the flux density, for given coil turns and current, by assuming that the reluctance of the iron part of the circuit has negligible reluctance relative to the airgap.

But if you have an airgap that is large relative to the dimensions of the pole then this is no longer true, and your force will be low (and difficult to calculate accurately).

If you need some help with the basic equations, please feel free to ask.

### RE: electromagnetic field measurement

(OP)
Again i thank you for your help.  However maybe I need to explain what I am doing a little more.  So I need to place something, say iron in a plastic chamber in the airgap, and I need to calculate the force on the piece of iron due to the electromagnet, and that is the equation I am having trouble with.  Now I can characterize the magnetic properties of the iron in the gap via a magnetometer, so I know the magnetization of the iron versus the magnetic field it is exposed to.

In an airgap, i know that the flux (B) is equivalent to the field (H) because in air, gauss and oersted are equal numerically.

Before you guided me to the c-shaped electromagnet, I was planning on calculating the force with the following equation
F=(H1-H2)*mu*m/t
F=force
H1-H2 difference in magnetic field across teh thickness of the iron sample
mu=permeability
m=magnetic moment of the iron
t=thickness of the sample.

Now, the c-shaped electromagnet will provide a much stronger magnetic field in the airgap, using the following equations provided in your other thread replies

reluctance S = g/(?0*A)
flux ? = NI/S  where N = no. of turns, I = current (A)
flux density B = ?/A  - in Tesla (1T = 10000G), A is airgap csa as above.

but now i need to go from B in the gap to the force on an object in the gap.

Also, those equations do not show an influence by whatever core is used in the electromagnet, is that correct?  I thought the core magnified the field?

Sorry, i guess the more I learn, the more complicated it seems.

George

### RE: electromagnetic field measurement

(OP)
I did find more info saying the same thing you said, with the same force equation you listed above, I guess i'm confused about...well, doesn't it matter what the material being attracted to the electromagnet is? Shouldn't its magnetic properties play a role on the force exhibited on it by the magnet?

Hmmm...

thanks,
George

### RE: electromagnetic field measurement

(OP)
As you can see, i'm trying hard to understand this...I don't know why I didnt think of this earlier.  So there is teh force equation between the poles of a magnet
F=(m1*m2)/(mu*r^2)
where m1 and m2 are teh pole strengths of the two magnets.
mu=permeability constant, and r is teh distance between poles.

Is is possible to find the "pole strength" of the electromagnet? and then use that equation, since i know the pole strength of my iron material from my magnetometer test?

Or am I off here...

### RE: electromagnetic field measurement

(OP)
Ok...one more and i think i should be off to bed soon.
So one book I had describes the force between two poles, like i mentioned before to be
F=(m1*m2)/(4*pi*mu*r^2) (in SI units)
or
F=(m1*m2)/(r^2) in cgs
(although the source I got the same equation listed above drops the 4*pi...)

and then it says the force can be described as the magnetic field generated by one pole acting on the second pole
so
F=(m1/r^2) * m2
H=m1/r^2

so then, can I take B in the gap...equate it to H, and solve for the force that way?  hmmm...I'm almost excited...
but this equation does not incorporate the cross section of teh magnet as the equation you listed does
F = B2*A/(2*?0)

If my method works, then the only question then is how come the equation for B for the electromagnet has no mention of whether or not there is a core to it?  Doesn't the core affect B?

I think i may have confused matters even more...

George

### RE: electromagnetic field measurement

George, I learnt my magnetics theory about 25 years ago (as part of an elec eng degree here in the UK), it was all mainstream SI units and that is all I've ever used since.  Maybe that is why I don't recognize some of your equations - for example the force equation you quote.  It may well be correct, but is it practical (in the same way as the Biot-Savart law is fundamental in describing the relationship between magnetizing force and current in a conductor, but only really used to derive more practical equations).

The number one point to understand in magnetics is that it is always based on circuits.  Flux lines always form closed paths; I'm sure you know this but it is vital.  That is probably why electrical engineers don't have a problem with magnetics, they are used to thinking of circuits.

From your latest description it sounds as though you have a piece of free-moving iron that you want to impart a force on.  This does make it a more difficult to calculate.  Imagine that you have two large iron pole pieces facing each other, forming part of a magnetic circuit and magnetic flux passing across the airgap between them.  If you introduce a piece of iron into the airgap, no force will be imparted on this piece!  There will be an attractive force between the two opposite pole faces, as described by the equation I quoted earlier, but assuming they are fixed then nothing will move including the iron piece (except due to gravity of course).  The reason it won't feel a force is because its motion will not change the stored energy in the magnetic circuit - that's the fundamental physics answer, a more practical way of looking at it is that it will only be forced to move if its new position reduces the total reluctance of the magnetic circuit (remember that reluctance is proportional to airgap length).  In effect you have two airgaps - one either side of the iron piece, if one closes then the other is opening, net result is no movement.  Incidentally, this even holds true if the free-iron piece is a permanent magnet (although there will be a rotational force trying to align its direction of magnetization with the main field).

So you need to think about how you can arrange the geometry of your electromagnet so that for the manner in which you want the iron piece to move (or at least feel a force) it acts to try and close the magnetic circuit by reducing the total length of all the airgaps in series in the magnetic circuit, i.e. reduce the total reluctance of the circuit.  For example the fixed poles of the electromagnet should be side-by-side rather than facing each other, so that both airgaps close at the same time.  I hope I haven't made that sound more complicated than it really is.

One other incidental point, yes it does matter what the material in the airgap is.  But in reality, provided all the components are appropriately sized (to avoid magnetic saturation), for most purposes there are only two types of material in magnetic circuits - non-magnetic (including air) and magnetic (including iron and ferrite).  The former has high reluctance, the latter very low reluctance (often treated as zero).  Total reluctance of the magnetic circuit is given by the algebraic sum of all the reluctances in series, so airgaps matter!

To reiterate, total flux is related to ampere-turns (mmf) by the equation:
flux = mmf/reluctance.

### RE: electromagnetic field measurement

(OP)
Aha...I that makes perfect sense...I thought there was something fishy in there.

So, I think then, I am back to a straight cylindrical solenoid electromagnet, because that will impart a force on anoter object and try to attract it to itself...it acts like a bar magnet.

And so I am back to trying to find the equation for B at a distance away from a cylindrical solenoid, on axis.  That equation exists, however, the equation is for just the solenoid shell (just the wires).  Adding a ferrite core dramatically increases the flux of the solenoid, but I don't know by how much.

The equation for B at a distance x from the end of a solenoid shell is
B=[(mu*i*N)/(2*l)]*[((x+l)/sqrt((x+l)^2+r^2))-(x/sqrt(x^2+r^2))]
where
i=current
N=number of coils
l=length of solenoid
x=distance from one end of solenoid (on axis)

the only thing funny about this equation is that the flux drop off is linear as you go away from the solenoid, and not exponential like I expected.  But it seems to be correct, i saw it in a number of sources.  I wonder though how to calcualte the increase in B due to an iron core.

That help was fantastic though, though!
Thanks
George

### RE: electromagnetic field measurement

(OP)
I think i found it...I think all teh iron core does is add a "k" factor to the flux density.  k being the relative permeability of the core, multiplying B by a factor of k.

Hmmm...I hope that is it!

George

### RE: electromagnetic field measurement

Hello George,

My copy of Hayt ("Electromagnetic Engineering"), normally my electromagnetics bible, doesn't give the equation for B on the axis of a solenoid, although I did find a version on-line:
http://www.netdenizen.com/emagnettest/solenoids/?solenoid
This is probably similar to your equation!
- alternatively a simpler form is the equation for B on the axis of a single coil (as derived from the dreaded Biot-Savart equation):
http://www.netdenizen.com/emagnet/solenoids/ilooponaxis.htm
which would give the value of B some distance away from the solenoid.  In both cases, B decreases linearly with distance, as you noted.
However this is a side issue, you want to calculate the force.

Whilst I certainly agree that the inclusion of a straight core inside the coil will give a big improvement in B (and I wouldn't know how to calculate it*, I would at this point be thinking about using FEA), I still think you should consider a C-core.  If you compare a bar magnet to a horse-shoe magnet, you will get a much stronger attractive force from the latter because there is very little air in the flux path.  The same is true of an electromagnet.

* if I had to take a stab at it, I would say that (by looking at the flux pattern) the total reluctance in the magnetic circuit with a core inside the solenoid is a bit less than one half of that without the core.  For a given number of ampere-turns this would give you about double the flux.  If the core completely fills the solenoid then the flux density within it is doubled.  I admit this could be wrong, I am suprised that the flux density isn't increased by more than a factor of 2.

### RE: electromagnetic field measurement

(OP)
Hey Pete, sorry for the hiatus.  I did see the solenoid equation from the netdenizen website (that is actually where I got the equation I listed above).

The reason I feel that I have to use a straight bar solenoid is because in order to attract another piece of iron, there has to be a gradient in the magnetic field seen by the iron across its thickness.  That difference would result from a gradient in the flux.  Like you pointed me to earlier, a c shape would have an almost consistent flux and would not create an attractive force on the iron.

This website seemed to help with how to calculate the flux of a solenoid with a core.  It seems that the core multiplies the flux by a factor.  that factor is basically how much more permeable the core is to magnetic field than air.  So they say for instance, the relative permeability of iron is 200 times that of air, then my flux would be amplified by 200 times.
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html#c5

I think that should help out my flux/field calculations.

Force then is basically the difference in the force exerted on each side of the iron piece I am attracting.  Basically, the side closer to the solenoid sees a certain attractive force due to the magnetic field (due to the flux).  The other side of the iron sees a repelling force (due to the dipole i guess) due to the magnetic field.  If the field is the same on both sides, the iron wont move.  If the field is different, then the iron will move.  Which is why I would need a bar, to have a gradient in the flux away from the magnet, across the thickness of the iron.

Force (SI) is a product of the magnetic field times the magnetic moment of the iron (due to a certain magnetic field), times the permeability constant divided by the thickness of the sample.  At least thats the way the conversions work out I think.  I dont have the original equation on me here.

Hmmm...what do u think?

George

### RE: electromagnetic field measurement

Hello again George.

re your comment "because in order to attract another piece of iron, there has to be a gradient in the magnetic field seen by the iron across its thickness":
this isn't true!  A force will result from a uniform flux density.  Maybe you are confusing it with magnetic vector potential, normally given the symbol A (as calculated directly in finite element analysis, subsequently converted to flux density B by differentiating A).  I have difficulty visualizing A, it's at the next level up in magnetic field concepts and you don't really need to think about it unless you are heavily into FEA.

re the link, I'm not happy about that.  It is true that replacing iron in the magnetic circuit can increase the flux density up to say 1000 times (for given ampere-turns) but only if iron replaces air for the WHOLE FLUX PATH.  In the case illustrated, only the core within the coil is iron.  For most of its path the magnetic circuit is still air, and this will dominate the total reluctance.

For an electrical analogy of the above, what you have is say a 1kohm resistor representing an air-core path within the coil, in series with a 1.5kohm resistor representing the path outside the coil (I've made it a bit larger because the path length outside is longer).  Now replace the air inside the coil with iron, you decrease the "resistance" (reluctance) of this part by 1000-fold to 1ohm.  But the total series circuit resistance has only gone down from 2.5kohm to 1.501kohm.  With a fixed "voltage" (ampere-turns) the "current" (flux) will only be increased by a factor of 2.5/1.501 i.e. less than 2.  Hope that makes sense.

To re-state my earlier comment, for maximum force get rid of as much air in the flux path as you can!

### RE: electromagnetic field measurement

I've studied removing magnetic particles from liquids and a magnetic field gradient is required to attract iron that is not itself already magnetized. In a uniform field would iron be attracted to the north or to the south pole? The answer is neither. Iron is generally attracted to the nearest pole because because the magnetic field gets stronger as you approach the pole from an air gap. It is this gradient that causes the attraction. A company that makes a very unique separator of this type has some technical info on their web site. http://www.sgfrantz.com/emdrywg.htm

### RE: electromagnetic field measurement

Compositepro, ok you have a valid point.  But the underlying fact remains that you don't need a large air path in the magnetic circuit to make the electromagnet work - in fact it is deterimental.

### RE: electromagnetic field measurement

(OP)
Oh no, I'm not thinking a larger airgap, but the C-shaped electromagnet will not work because it has a uniform flux path.  And actually your example makes a lot of sense (thanks!).  But say I surround the electromagnet with a permeable material (reducing the reluctance).  I think this will pull in the flux lines more quickly back into electromagnet.  True, it would make it stronger, but it would also weaken significantly more quickly as you go away from the face of the magnet.  I need a strong field at a distance away from the magnet.  therefore I think I should just have the iron core in the electromagnet. make it as strong as I can and still allow it to extend beyond the end of the magnet, almost in a similar method as you would trying to pick up something without touching it (or separating from a distance, like composite mentioned.)

### RE: electromagnetic field measurement

The force acting on a mobile entity, that responds to a magnetic field, is proportional to the product of the field magnitude and the gradient of that field, at that point in space.  So to maximize the force, you need to maximize this product - the easiest way is to use a "reasonable" value for each part of the equation, rather than a low value for one and a high value for the other.

Gareth P. Hatch, Ph.D.
Director of Technology
Dexter Magnetic Technologies
http://www.dextermag.com

### RE: electromagnetic field measurement

George, I must put my hands up and say I was wrong when I said that the force wasn't proportional to the gradient of flux density.

Gareth, I take your point although you will agree I think that to get a reasonable value for field magnitude you do want to minimize the length of the air path - even a small airgap drastically reduces the flux density.  It has never been normal practice to deliberately introduce longer air paths in order to increase the attractive force (although there may be special circumstances when you might do so, such as a requirement for linearity of force).

So I stick to my original point, minimize the airgaps.  Taking for example a large active magnetic bearing such as manufactured by my employer (but not designed by me!) the total flux path for each pole is approximately 0.5m but the two airgaps are just 1.3mm, the mechanical clearances to allow shaft rotation.

### RE: electromagnetic field measurement

Yes George - I agree that if the system can cope with a minimal air gap, that's a good approach to take.

Generating large forces within smaller volumes though, is where permanent magnets just can't be beat, particularly if you put two magnets together side by side - the gradients become the dominant term in the force equation.

Gareth P. Hatch, Ph.D.
Director of Technology
Dexter Magnetic Technologies
http://www.dextermag.com

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