[scientizscht (OP)]

Hello!

At which extend we can manipulate magnetic fields?

For example, can I choose a specific shape and size of space and put magnets in the right positions so that the magnetic field in that space will be as I want it to be?

In other words, can we design magnetic fields in a specific space and then produce it? With permanent magnets?

Thanks

[Kryptid]

There are constraints on how you can construct a magnetic field. Two poles must always be present and the fields lines must link these poles. Earnshaw's theorem also forbids the construction of a static magnetic field from permanent magnets that results in the passive levitation of another permanent magnet: https://en.wikipedia.org/wiki/Earnshaw%27s_theorem

[Bored chemist]

Earnshaw was misinformed, his view was classical.
Quantum mechanics lets us have diamagnetic materials.

[Kryptid]

Earnshaw was misinformed, his view was classical.
Quantum mechanics lets us have diamagnetic materials.

If I'm not mistaken, he was speaking of paramagnetic and ferromagnetic materials.

[evan_au]

At which extent we can manipulate magnetic fields?

Not nearly as well as we can manipulate electrical flows.

We have very cheap and effective electrical conductors like copper metal (with very high current density), and very cheap and effective electrical insulators like PVC plastic (with very high breakdown voltage). The ratio in electrical conductivity must be in the billions.

We have fairly expensive magnetic "conductors" like mu-metal (but they saturate very easily). We don't have very good magnetic insulators, much better than air or vacuum. The ratio in permeability is a thousand or so, but only in very weak magnetic fields.

If cost is no object, you can use superconductors to provide magnetic shielding, as the Meissner effect excludes a magnetic field - provided the magnetic field is not too strong, and the frequency of the magnetic field is not too high. And it only works properly in "Type 1" superconductors, which require really cold temperatures.

See: https://en.wikipedia.org/wiki/Meissner_effect

[PmbPhy]

Two poles must always be present and the fields lines must link these poles.

That's not true. E.g. when a magnetic field is created by time altering electric fields or by steady currents there's no need for a pole. Take the magnetic field generated by a wire wrapped around a torus as an example or a straight current carrying wire - or any static field created by currents.

[Kryptid]

That's not true. E.g. when a magnetic field is created by time altering electric fields or by steady currents there's no need for a pole. Take the magnetic field generated by a wire wrapped around a torus as an example or a straight current carrying wire - or any static field created by currents.

This is new information to me. So what would happen if I held the north pole of a bar magnet up to this toroidal electromagnet you mention? Would it be attracted or repelled? Would the same occur if I held the south pole up to it instead?

[Colin2B]

This is new information to me. So what would happen if I held the north pole of a bar magnet up to this toroidal electromagnet you mention? Would it be attracted or repelled? Would the same occur if I held the south pole up to it instead?

You can check it out by using a compass near a wire carrying dc current, the compass will align itself along the magnetic field lines. I seem to remember doing this at school.
Look up Flemimgs Right hand rule

[alancalverd]

There are constraints on how you can construct a magnetic field. Two poles must always be present and the fields lines must link these poles. Earnshaw's theorem also forbids the construction of a static magnetic field from permanent magnets that results in the passive levitation of another permanent magnet: https://en.wikipedia.org/wiki/Earnshaw%27s_theorem

Unless you buy it from Amazon, of course (other suppliers are available)

61Ev4kvwv7L._SX679_.jpg (49.21 kB . 679x679 - viewed 2795 times)

[alancalverd]

Anyway, we can use permanent magnets to construct a sufficiently homogeneous magnetic field to allow magnetic resonance imaging, and we tweak that field by adding "gradient" fields generated by electromagnets to select and read the proton resonance at a particular point in the patient. Permanent magnets are unfortunately too bulky and temperature-sensitive to extend the primary field much beyond 0.3 Tesla so modern MRI machines use electromagnets, either temperature controlled or superconducting, to reach 3T or more.

We can also use "active shielding" to cancel stray magnetic fields entering the MRI room - handy if you have passing traffic or, in one case I worked on, an underground railway station next door.

But as Evan says, it's a lot harder to manipulate magnetic fields than electric fields. When you squish the field lines at A, they tend to pop out at B. Herding rubber cats is easier.

[Bored chemist]

This is new information to me. So what would happen if I held the north pole of a bar magnet up to this toroidal electromagnet you mention?

This
https://en.wikipedia.org/wiki/Homopolar_motor#/media/File:Faraday_magnetic_rotation.jpg

I think the strict criterion might be that there must be an even number of poles.

[evan_au]

Two poles must always be present and the fields lines must link these poles.

I think the criterion is that the magnetic field lines must always form a closed path*.
- In a bar magnet, the closed path extends from south pole to north pole, and back through the body of the magnet to where they started.
- I have used toroidal inductors as current transformers, and they are very effective at containing their magnetic field. In this case, the closed path runs in a ring through the toroid.
- In a straight wire carry a DC current, the closed paths are concentric with the wire. See Ampere's Right-Hand rule
https://en.wikipedia.org/wiki/Right-hand_rule#Amp%C3%A8re's_right-hand_grip_rule

My recollection is that magnetic fields have the mathematical property of "curl", which means they form closed loops; and they don't have the mathematical property of "divergence", which means that they don't start or stop at a point*.
See: https://en.wikipedia.org/wiki/Magnetic_field#Maxwell's_equations

*This assumes that there is no such thing as the hypothetical magnetic monopole. There have not been repeatable detection of magnetic monopoles, despite several searches, some of which claimed to detect "hits".
See: https://en.wikipedia.org/wiki/Magnetic_monopole

[evan_au]

So what would happen if I held the north pole of a bar magnet up to this toroidal electromagnet you mention? Would it be attracted or repelled? Would the same occur if I held the south pole up to it instead?

For low frequency applications (eg 50/60Hz), you could make the toroid by winding a strip of high-permeability alloy (like Mu-metal) into a reel.
- For high frequency applications (eg 1-100 MHz), you could make the toroid by moulding a ferrite powder.
- You then wind a copper coil around the toroid, spacing the copper windings out evenly around the perimeter.
- Both toroidal core materials are ferromagnetic, so they would attract the north or south pole of a permanent magnet that was placed nearby.

This attraction applies if:
- There is no current flowing through the copper winding. The magnet is attracted to the toroidal core.
- There is AC or DC flowing through the copper winding. This magnetic field from the electromagnet is contained within the toroidal core.
 
But you would try to keep a permanent magnet and DC currents away from Mu-metal, as it saturates easily, and then loses most of its desirable magnetic properties.

In the current transformer application, you pass the "high current" winding (eg 0-100A at 50Hz) through the center of the toroid; this effectively makes a "1 turn" winding, even if you have to trace it back to the power station.
- There is also a "low-current" winding; if this has 1,000 turns, then it will produce 0-100mA at 50Hz.
- Note that you must never operate a current transformer with the low-current winding "open circuit", as it can produce high voltages that are a risk to personnel, and it will probably destroy itself by arcing over.
See: https://en.wikipedia.org/wiki/Current_transformer#Function

[Kryptid]

Unless you buy it from Amazon, of course (other suppliers are available)

61Ev4kvwv7L._SX679_.jpg (49.21 kB . 679x679 - viewed 2795 times)

That isn't passive levitation. I own a similar device and it uses sensors to rapidly vary the strength of electromagnets in order to keep the tiny Earth in place.

[alancalverd]

Interesting. But the question was about levitation, not controlled levitation!

Imagine two bar magnets with their north poles opposed. They will be pushed apart. Now constrain them in a  vertical tube: levitation!

Not to be confused with the Meissner effect, which is inherently stable over a small range of movement.

[Kryptid]

Interesting. But the question was about levitation, not controlled levitation!

Imagine two bar magnets with their north poles opposed. They will be pushed apart. Now constrain them in a  vertical tube: levitation!

I'm not sure how much more specifically I need to qualify my statements. Earnshaw's theorem applies to idea of static ferromagnets suspended in free space solely due to the force of their own fields, not levitating within physical restraints like a tube. I also don't think the OP asked about levitation specifically. It's just something I brought up.

[wolfekeeper]

If you're being strictly accurate, Earnshaw's theorem applies to magnetic fields where the relative permeability mu is precisely 1. For example copper electromagnet coils are very close to that.

When mu is other than 1, Braunbeck's extension to Earnshaw's theorem shows that mu below 1 allows magnetic levitation and when it's greater than 1, it's further destabilising. Neodymium magnets are slightly above (mu = ~1.2).

Anyway, the answer to the question is, can you manipulate magnets however you want. Yes, pretty much, but the freespace field is subject to:

∇.F = 0

for any magnet

[scientizscht (OP)]

OK so we agree that we cannot manipulate magnetic fields and construct a specific magnetic field, as easy as electric fields.

Can you tell me how we can construct an electric field of eg the shape of a cylinder of specific dimensions?

[wolfekeeper]

Make a metallic cylinder that size. Charge it. The end.

[evan_au]

oops - overlap with wolfekeeper...

how we can construct an electric field of eg the shape of a cylinder of specific dimensions?

An electric field will have no effect on uncharged particles.
- An electric field gradient can attract or repel a charged particle.
- Note that practical electric fields do not exist in one place, and suddenly drop to zero - they tend to have a gradient, or terminate on a conductive surface (eg a metal shield).

The simplest way to produce a cylindrical electric field is to take a metal cylinder, and charge it (positive or negative)
- The electric field will have a roughly cylindrical shape outside the cylinder, decreasing in strength with distance
- The electric field will be zero inside the cylinder
- If you want to shape the electric field more precisely, you can use a plastic dielectric around the cylinder - but charged particles don't tend to move inside a plastic dielectric
- You need to hold it in an insulating vacuum, or the charge will leak away (even in a vacuum, cosmic rays or UV light will cause it to leak away eventually...)
- Or you could connect to to an electrical circuit that keeps it charged, relative to some fairly neutral object like the Earth

For this design, there will be some deviations from a perfect cylindrical field, because if you charge the metal cylinder negatively, all the excess electrons will try to get as far from each other as possible - which means there will be more of them at the farthest extremities of the cylinder.

To design something accurately for a specific purpose (eg for the LHC), it is best to use some simulation software that helps you model electric and magnetic fields, so you can optimise your design.

I am sure there are many such tools around, including free ones; one I have heard of is here. I am sure @alancalverd has seen some suitable tools in his line of work.