# What core design of an electromagnet will maximize field at more distance

• dlbeeson
In summary, the core design of an electromagnet that will maximize the field at a greater distance is one with a smaller magnetic reluctance and a larger number of turns. This means using a material with high permeability, such as iron, and increasing the number of coils in the magnet. Additionally, using a power source with high voltage and low resistance can also help to increase the strength of the field and extend its reach. Finally, shaping the core into a longer, thinner design can also improve the magnet's performance at a distance.
dlbeeson
Given the same voltage and current, hence electrical power, what kind of core design can maximize the "reach" of an electromagnet? For example, with the magnet above a table, axis pointing down at the table, attempting to lift a small iron washer, is there a core design that significantly increases the distance the electromagnet can be raised and still lift the washer? Is just a cylindrical core best? Would a horseshoe core with a winding on each leg (though same electrical power as other cores) reach farther? Or could a conical core with the "down" end having a smaller face shape the magnetic lines of force to reach out farther, using the same electrical power as other cores?

Wide and flat will have a field that 'reaches furthest'. A horseshoe is quite the reverse as it has a strong field between the poles and not much anywhere else. Look at magnet field patterns (images) on google to get an idea. When a piece of steel is magnetised, the 'poles' are not just on the end faces (the pole is only a region where the lines appear to concentrate).
The problem is that a magnetic field drops off quicker with distance than the inverse square field law of a point charge or mass. The two poles are acting 'against each other' once you get a fair distance away.

Electromagnets are very good for holding on to an object but not good at attracting it from a distance because of the way the field drops off.

I agree but if you make the end very wide won't the field density be low? In which case a cone shape tip will help concentrate the field. Presumably there is an optimum area given a fixed power input?

cn_2149
If you manage to make a small region at the end with a very high field strength around it, that field will rapidly spread out and become low very quickly. If you have a wide area of pole, the field will not spread out as fast so, with an initially low field, you can end up with less fall-off at a distance.
So you takes yer pick. You can extend the range if you can do without a high flux near the pole.

dlbeeson said:
Given the same voltage and current, hence electrical power, what kind of core design can maximize the "reach" of an electromagnet? For example, with the magnet above a table, axis pointing down at the table, attempting to lift a small iron washer, is there a core design that significantly increases the distance the electromagnet can be raised and still lift the washer? Is just a cylindrical core best? Would a horseshoe core with a winding on each leg (though same electrical power as other cores) reach farther? Or could a conical core with the "down" end having a smaller face shape the magnetic lines of force to reach out farther, using the same electrical power as other cores?

This really is a bit of a contradiction, as the whole point of core inside an electromagnet coil is to concentrate and contain, as much as possible, the magnetic field within the core/coil

Dave

davenn said:
This really is a bit of a contradiction, as the whole point of core inside an electromagnet coil is to concentrate and contain, as much as possible, the magnetic field within the core/coil

Dave

A core will increase the flux too - and reduce the 'leakage' between turns. The only way to get a benefit is to have a big area if you want to 'tailor' the field. Also, the longer the electromagnet the better - the distance at which the effects of the two poles becomes comparable gets greater and greater, the longer you make it.

Thank you sophiecentaur, CWatters, and Davenn.
I did Google images of magnetic fields and flux lines and that did eliminate the horseshoe design. From your responses I gather that wide, flat, and long is best. That seems to mean that a flat faced, large diameter, core will cause the field to "reach out" farther than a smaller diameter, core with the same current and voltage. That would mean the same power, and by increasing the wire guage, the resistance would be decreased, so the same number of windings, needing more wire length for the larger diameter, could still draw the same current.

So your responses seem supported by the equation Force = ((N x I)^2 x k x A) / (2 x g^2). I do now see that as the cross-sectional area of the magnet face increases, so should the Force. This equation however says nothing about the axial length of the core. Is "the longer the electromagnet the better" have some easy formula like this one for helping to calculate before building?

The point about most electromagnet design is that they are not usually considered as suitable for acting at a long distance. The field inside a coil is used for guiding and focussing particle beams and working actuators - 'cos it's 'good engineering'.
What you are after is a bit of a 'fringe activity' so you need to be thinking a bit differently.
You don't want a high field - you want a remote field which is way outside the actual device (so I believe).
Power is not a fundamental issue - except to overcome resistive losses. There is no continual power supply needed to maintain the field - it just needs energy to set it up. Depending upon how much money you have (to buy the copper), because you are not constrained by size, you can use as many turns of wire as you like and have a large area.
Where did this come from?
Force = ((N x I)^2 x k x A) / (2 x g^2)
What is the Force, you refer to?
The field for a solenoid is given in this link, which tells you the field inside the solenoid - where it's just the density of windings that counts. This is the easiest field to calculate and you see that it doesn't matter what the area is. B is the Flux Density and the total Flux is given by B times the area. Clearly, a large area can produce more force because the force on a wire, for instance, depends on the length of wire - which depends on the extent of the field.
I found this link which shows how to work out the field on the axis of a solenoid, beyond the ends of the coil. You can see how the length is important and also the radius. That link may be what you want. in fact. Whatcha think?

Thank you for your response and help.
The Force is the magnetic pull force, in Newtons.
k is the permeability constant of air =µ0 = 4p×10-7 V·s/(A·m)
Found the formula here. I do note the response questions its accuracy.
The original source is given as:
http://www.ehow.com/how_10000466_calculate-weight-electromagnet-can-pull.html
And this short article is exactly what I want, EXCEPT, it seems to give no thought to core design, Hence my question about the core design.

Sophiecentaur, if I may bare my soul to you without scaring you away, the underlying reason for the question is the transmission of power short distances of 6 to 10 feet.
I build wall hanging bubble aquariums. With no air pump, only a few certain fish can be supported, and a light enhances the beauty. Lights and air pumps require an ugly hanging electrical wire dangling down the wall, or a cost to install an electrical outlet behind the aquarium. Batteries would be a horrible hassle. I want to go wireless!

Building codes seem to require an electrical outlet every 12 feet, so the maximum horizontal distance is about 6 feet. Outlets are about 1 foot off the ground, and the highest the aquariums are hung is about 7 feet high, giving a vertical distance of 6 feet, and with the max horizontal distance of 6 feet, the Pythagorean Theorem gives me an 8.5 feet maximum target distance.
Power for a small air pump comes from 2 D batteries, and with a Joule Ringer I have powered a 15 watt CFL bulb continuously with a AA battery. A standard Carbon-zinc D Cell can deliver 18743 joules and an AA 2340 joules, so, doubling the D cell, I need 39826 joules as my minimum target, at 8.5 feet.

I am trying to experiment with a transmitter that plugs in and hangs from a standard wall outlet, and transmits the 40 K joules needed to 8.5 feet. Most wireless power transmission systems I see on the web go high freq air core and are low power. I don't want licensing issues, so would like to stay ultrasonic or under.
A standard transformer is extremely more efficient with NO AIR GAP between primary and secondary. So, in my simple thought process, somewhere there is a distance where separating the primary half core away from the secondary half core (as in a toroidal core cut in half axially) will still be better at 60 hertz (or some sonic or ultrasonic freq) than building a high frequency air core transmitter.

Hence my question on the electromagnet "reach", as the primary winding and half core of the transmitter would be more like an powered electromagnet reaching out to a second electromagnet that is receiving the field as a transformer "remote" secondary. The separated half toroids would seem, as distance between (air gap) increased, to model a horseshoe core, and pull IN the lines of force, not send them out. A standard long (6 inch?) rod(0.5 inch dia.) seems like my starting point core design. Or do I have to go coreless and high freq?

Yes, I am an experimenter, and will experiment, but I don't want to waste too much time on dead ends, and therefore would like some theoretical starting point.
If you can offer any guidance, I would greatly appreciate it.

Hi again
Yes - that equation you quoted is a bit suspect - not really applicable to your purpose (very specific, I think). The formula in my link is the nearest you will get, I think.
But, from what you now say, we are chasing a red herring here by talking of electromagnets.
You really ought to look into / search "Wireless Power" for this - the static field around a coil is only a part of the consideration. You will need a high frequency system and resonant coils. Relatively close wireless is more like a large, air spaced transformer.
You could waste a lot of time in experimenting if you don't make use of what's been done already. Search this forum, for a start.
I'm afraid that I am not very enamored with the Wireless Power topic because of the airy fairy way many of its followers treat the subject and their 'explanations' can be entertaining - quoting Tesla in revered terms, etc.. But that's just my view.
I must say, if you need to get power from a fixed source to a fixed target and there is not a ravine full of crocodiles or the like, in the way, then wireless is a very hard way to achieve it. You can do some very good cosmetic hard wiring with a small fraction of the effort you'd need for a wireless link - and wires WILL work and require no maintenance. Your aquaria need to be supported somehow. Can't the power get to them via the supports? Are you planning to sell this system? If so, it will need to be reliable and satisfy FCC regulations for interference.
I could suggest that you consider asking yourself why, if this can be done easily - or even at all, it's not available in the shops. We still have charging leads for out phones and computers etc etc. For a couple of hundred quid, most people would buy the wireless facility if it were available. But none is available. Think of the fantastic tech that we buy without a second thought, these days. If it's possible, they sell it six months after it's been invented.

Sophiecentaur,
Thank you again!
Yes, perhaps wireless is the long way around.
And of course you are right that wires are easier, and cheaper.
Yet, to be able to allow someone to just hang an aquarium on any wall, anywhere in their home, in any artistic arrangement does seem compelling to me.
Their only choice now is either wires either stapled to the wall, or in a plastic wirerun, or to hire a handyman to install an outlet at the point they want their tank.
I would like to find out just how hard and expensive it is before giving up the idea.
I shall do as you suggest and search this forum.
So thank you again, very much, for your guidance, advise, and help.

I have read that a magnetic field increases the permeability of the core. Is this true of an air core? If so, will a permanent magnet aligned to pick up the iron washer on the table, but not strong enough to do so alone, still increase the permeability of the air path from the electromagnet to the washer, so that less electrical power is required by the electromagnet that is behind or in front of the permanent magnet. I understand the permanent magnet and the electromagnet forces will add together, but I am asking if the permeability increase in the air path by the permanent magnet actually gives the electromagnet more force for less electrical energy because of a more permeable air core path to the washer laying on the table?

I have FEMM and QuickField mag field plotting programs, but is there some simple interface like

but where you can change the core length and width by clicking and dragging, and change the coil turns and current similarly, and with a little higher resolution field lines?

dlbeeson said:
I have read that a magnetic field increases the permeability of the core. Is this true of an air core? If so, will a permanent magnet aligned to pick up the iron washer on the table, but not strong enough to do so alone, still increase the permeability of the air path from the electromagnet to the washer, so that less electrical power is required by the electromagnet that is behind or in front of the permanent magnet. I understand the permanent magnet and the electromagnet forces will add together, but I am asking if the permeability increase in the air path by the permanent magnet actually gives the electromagnet more force for less electrical energy because of a more permeable air core path to the washer laying on the table?

Where did you read this? afaik, in a linear material, the permeability is a property of the material and not the applied field.

Electrical Review, volume 71 by George Worthington available here:
on page 887 States "the absolute permeability of different substances varies in the case of magnetic materials with the flux density, as is obvious from the consideration of the fact that the reluctivity of magnetic substances varies with the flux density."

and on page 886 gives a chart showing just that, it seems to me.

Also At:
http://en.wikipedia.org/wiki/Permeability_(electromagnetism)
it states:
"In general, permeability is not a constant, as it can vary with the position in the medium, the frequency of the field applied, humidity, temperature, and other parameters"

Note the "at a magnetic flux density of 0.002 w/m^2" beside the table in this link.

http://hyperphysics.phy-astr.gsu.edu/hbase/solids/ferro.html#c5

That seems to indicate the permeabilities would be different at other flux densities.?.?.?

By the way, this chart gives iron's relative permeability as 200, and permalloy as 8,000.

Does that mean an electromagnet with a permalloy core would have a 40 times stronger magnetic field at a given electrical power, as long as the core is not saturated?

dlbeeson said:
Note the "at a magnetic flux density of 0.002 w/m^2" beside the table in this link.

http://hyperphysics.phy-astr.gsu.edu/hbase/solids/ferro.html#c5

That seems to indicate the permeabilities would be different at other flux densities.?.?.?

I really don't think so - at least, within the linear region. I don't know how this all relates to remanence in permanent magnets, though.

Magnetic field produced by any configuration of magnets is a summ of fields of each individual magnet.
So, for the long distance (much bigger than system size), best, when every submagnet turned by the same pole, and not a big difference whether it is a tube or plate.

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Graniar said:

Magnetic field produced by any configuration of magnets is a summ of fields of each individual magnet.
So, for the long distance (much bigger than system size), best, when every submagnet turned by the same pole, and not a big difference whether it is a tube or plate.

You are right about "force line manipulation". Field lines are the result of fields and not the other way round.
With increasing distance, what you say becomes a good approximation of what happens but the near field pattern is very much determined by the spatial arrangement. A wide array of charges, antennae, masses and magnetic poles will give a more even spread of field locally - which is what the OP was after, afaics. A good wide one beats a good narrow one any day.

sophiecentaur said:
A wide array of charges, antennae, masses and magnetic poles will give a more even spread of field locally - which is what the OP was after, afaics. A good wide one beats a good narrow one any day.

Ok, for local fields configuration is a point. But what is an optimal configuration if the goal is to get maximum strength at the point?

I think this one, where point is surrounded with properly oriented elementary magnets. Due to cubic decreasing of field, there is a logarithmic dependence of multiplication achievable to outer/inner radius of such a sphere

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Graniar, thank you. Nice focusing of the field!

Graniar, so back to the original question, in an electromagnet, what core design will send the field out farther in 1 direction or axis? A long cylindrical core? A short fat cylindrical core with a pancake coil winding? A Cone shaped core with the point toward the washer to be picked up? What do you think?

dlbeeson said:
Graniar, so back to the original question, in an electromagnet, what core design will send the field out farther in 1 direction or axis?

That design, where all domains will be oriented parallel to that axis, and it's definately not a cone. Form is not a big deal (If only allow some parts of it to be a bit closer to the target) Remind of the cubic decrease in distance. 10 times farther means 1000 times weaker.

By the way, scaling would work well. If IE 1sm magnet generates some field on a 10sm distance. Huge 1m magnet of same form would generate field of same strength on a 10m distance

## 1. How does the number of turns in an electromagnet's coil affect its field strength at a distance?

The number of turns in an electromagnet's coil directly affects its field strength at a distance. As the number of turns increases, the magnetic field also becomes stronger. This is because each turn in the coil adds to the overall magnetic field, creating a stronger and more concentrated field.

## 2. What is the impact of the core material on the field strength of an electromagnet at a distance?

The core material of an electromagnet plays a crucial role in determining its field strength at a distance. A core material with a high magnetic permeability, such as iron or nickel, will increase the magnetic field strength, while a non-magnetic core material, like copper or aluminum, will have a weaker effect on the field strength.

## 3. Does the shape of an electromagnet's core affect its field strength at a distance?

Yes, the shape of an electromagnet's core can impact its field strength at a distance. A longer core will allow for more turns in the coil, increasing the field strength. Additionally, a core with a larger cross-sectional area will also contribute to a stronger magnetic field.

## 4. How does the current flow through the coil affect an electromagnet's field strength at a distance?

The current flow through the coil is directly proportional to the strength of an electromagnet's field at a distance. Increasing the current will result in a stronger magnetic field, while decreasing the current will weaken the field.

## 5. Can the distance between an electromagnet and a target affect the field strength?

Yes, the distance between an electromagnet and a target can impact the field strength. As the distance increases, the field strength decreases due to the spreading out of the magnetic field. This decrease in field strength follows the inverse square law, meaning that the field strength is inversely proportional to the square of the distance between the electromagnet and the target.

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