Hollow Spherical Magnet: Construction, Magnetic Field and Interactions Explained

[Harmony]

Is it possible, thematically or practically, to construct a hollow spherical magnet with inner surface and external surface of opposite polarity? How would the magnetic field looks like?

Assuming it is possible, what would happened if I place a smaller hollow spherical magnet, but of the opposite polarity, in the larger spherical hollow magnet?

Thanks in advanced!

 

[Vanadium 50]

It is not possible.

 

[captn]

It is not possible.

Any explanation as to what prevents it?


Neil

 

[csprof2000]

It would be a magnetic monopole. I think that most physical theories have it that these don't exist.

I know that's not an entirely satisfactory answer.

I think an interesting exercise may be to assume you have such a system, and applying the boundary conditions of magnetostatics, show that B or H is zero both inside and outside the shell... I'm sure this is what would happen. Why? Because it seems obvious to me that you could jury-rig a sphere using modified bar magnets, but the result cannot be magnetized. Ergo, zero B-field.

Other ideas?

 

[captn]

It would be a magnetic monopole. ...

...seems obvious to me that you could jury-rig a sphere using modified bar magnets, but the result cannot be magnetized. Ergo, zero B-field.

Bar magnets is what I was thinking...I was wondering if the repulsive energy would cause a reversal of the field on one (weak) side.

I'm embarassed that I didn't think of the monopole!


Thanks, Neil

 

[Harmony]

It would be a magnetic monopole. I think that most physical theories have it that these don't exist.

I know that's not an entirely satisfactory answer.

I think an interesting exercise may be to assume you have such a system, and applying the boundary conditions of magnetostatics, show that B or H is zero both inside and outside the shell... I'm sure this is what would happen. Why? Because it seems obvious to me that you could jury-rig a sphere using modified bar magnets, but the result cannot be magnetized. Ergo, zero B-field.

Other ideas?

Thanks for the prompt replies. Yeah, I think that even if we manage to forge such a magnet, the magnetic domain will probably rearrange again.

Is it correct for me to generalise that we can never make a hollow closed-surface magnet with exterior and interior of the opposite polarity?

What if the surface is not entirely closed? (eg. A sphere with a hole) I am not sure how to calculate the magnetic field of such system, perhaps the maths is far beyond my reach

Also, has anyone succeeded in creating a pseudo magnetic monopole yet?

 

[Vanadium 50]

The field line configuration you are trying to create is not consistent with the equations describing how magnetic fields behave. (Specifically that the divergence of the magnetic field is zero).

 

[Harmony]

The field line configuration you are trying to create is not consistent with the equations describing how magnetic fields behave. (Specifically that the divergence of the magnetic field is zero).

I found this online:
http://farside.ph.utexas.edu/teaching/em/lectures/node35.html

Hmm...so the div B cannot be zero if Maxwell Equations are correct (No magnetic monopole). But is the statement equivalent to pseudo magnetic monopole (any arrangement of dipole that partially resemble a monopole) cannot exist? (I remember that I read somewhere that some condense state matter resemble magnetic monopole partially)

 

[berkeman]

Thanks for the prompt replies. Yeah, I think that even if we manage to forge such a magnet, the magnetic domain will probably rearrange again.

Is it correct for me to generalise that we can never make a hollow closed-surface magnet with exterior and interior of the opposite polarity?

What if the surface is not entirely closed? (eg. A sphere with a hole) I am not sure how to calculate the magnetic field of such system, perhaps the maths is far beyond my reach

Also, has anyone succeeded in creating a pseudo magnetic monopole yet?

Please build your magnetic field with dipole sources. What kinds of fields can you make?

 

[csprof2000]

As long as the surface isn't closed, it may be possible. I would guess it would look something like the attached picture. Thoughts?

 

[RApsimon]

Consider theoretically constructing the sperical magnet as a series of normal bar magnets (consider 2-dimensions for simplicity). If you have two bar magnets opposite each other along the x-axis with like poles facing (N against N, or S against S). The field lines between the magnets diverges along the y-axis.

Add two more bar magnets (like poles facing) along the y-axis. Now the field lines diverge between the gaps either side of the magnets. You can probably see where this is going now...

As you increase the number of bar magnets, the field lines diverge between the gaps. Let's take this model to the infinite limit; you have an infinite number of infinitesimal bar magnets forming a sphere. The field lines would "squeeze" between the gaps, but in the infinite limit, this actually means that the field lines reverse direction entirely.

The result is that the field lines go back into the magnet and cancel themselves. Therefore the field is zero everywhere; hence no monopole!

 

[mikeph]

Try applying Stokes theorem on the electric currents over each half of the circle (in the case of constructing this thing from a bunch of outward-facing bar magnets) - the current going around the equator due to one hemisphere is equal to the sum of the currents at each point on the surface, which will exactly cancel the current going around the equator due to the opposing surface. So there will be no net current, and no magnetic field.

 

[RApsimon]

To MikeyW.

The problem with your approach (as it stands) is that the magnetic field isn't varying in time, so the Maxwell-Faraday equation tells you that there is no electric current. I don't think this alone tells you anything about the existence (or lack thereof) of the magnetic field.

Your approach does however work if you consider each infinitesimal bar magnet to be an electromagnet connected to an AC current. In this case, the polarity of the magnets would vary sinusoidally, producing your electric field. And then, as you stated, the currents will zero at all times because the entire spherical shell is an equipotential.

I certainly like your elegant way of looking at this problem

 

[mikeph]

The problem with your approach (as it stands) is that the magnetic field isn't varying in time, so the Maxwell-Faraday equation tells you that there is no electric current.

Any magnetic field - static or nonstatic - is generated by a current. A bar magnet is a current loop, so I'm picturing a sphere consisting of an infinite set of infinitesimal current loops on its surface. Each one is fully canceled by its neighbours, and because the surface is closed, there are no loops without neighbours to cancel - no net current.

 

[RApsimon]

ok, I see what you mean, thanks for the clarification