What magnetic fields can this hollow rod shield?

[Lotto]

TL;DR

I have a hollow rod capable of shielding a magnetic field and inside it I have a magnet. What magnetic field can the rod shield? Only an external one or the field of the magnet as well?

I suppose it can shield only the external magnetic field, not the field of the magnet itself. But I am not completely sure.

 

[osilmag]

Since the hollow rod has the same properties inside and outside, it should shield from external and contain the internal field too.

 

[tech99]

Since the hollow rod has the same properties inside and outside, it should shield from external and contain the internal field too.

I think it would need to be longer than the magnet to be effective and to have good magnetic properties.

 

[berkeman]

TL;DR Summary: I have a hollow rod capable of shielding a magnetic field and inside it I have a magnet. What magnetic field can the rod shield? Only an external one or the field of the magnet as well?

I suppose it can shield only the external magnetic field, not the field of the magnet itself. But I am not completely sure

So when you are thinking about magnetic shielding scenarios, it's important to remember that the principle being used is that magnetic B-fields are diverted to higher $\mu$ regions (like inside ferrous metals or high-mu shields). So nothing magical is going on; you are just designing your "shield" geometry to intercept and divert B-field lines to guide them around your region of space that you want to keep free of that B-field.

So your ferrous cylinder can help to "shield" the inner region from external B-fields (assuming that the ferrous shield material is not saturated by the strength of the external B-field). But it will do very little to "shield" the B-field from a magnetic inside the cylinder, other than to attract and guide the B-field. So the position of the magnet inside the cylinder compared to where you want to "shield" would be important.

Here are a couple good resources to help you learn about magnetic shielding:

** Magnetic Shield Corporation makes mu-metal magnetic shields (I have used their services several times in my EE work), and their website has good resources for learning more about shielding basics:

https://www.magnetic-shield.com/all-about-shielding-faqs/

** Here is an old PF thread where magnetic field basics were discussed:

https://www.physicsforums.com/threa...core-are-in-a-external-magnetic-field.991887/

 

[tech99]

In this case the diagram is not correct however bevause the magnet is aligned with the axis of the cylinder.

 

[berkeman]

In this case the diagram is not correct however bevause the magnet is aligned with the axis of the cylinder.

I think the magnet inside the cylinder in the OP's scenario is likely meant to be aligned with the cylinder's axis, true. So those field lines would be pretty different, but still attracted to the high-mu material of the cylinder. The figure I posted was meant to be a general illustration for how B-field lines are deflected into regions of higher $\mu$.

 

[Lotto]

I think the magnet inside the cylinder in the OP's scenario is likely meant to be aligned with the cylinder's axis, true. So those field lines would be pretty different, but still attracted to the high-mu material of the cylinder. The figure I posted was meant to be a general illustration for how B-field lines are deflected into regions of higher $\mu$.

And if we have a bar magnet inside the rod, what would induction lines of the magnet look like? Like induction lines of the magnet outside? Could I use the same equations for describing it?

 

[berkeman]

And if we have a bar magnet inside the rod, what would induction lines of the magnet look like?

If you have a bar magnet oriented along the hollow metal cylinder's axis, the field lines will use the cylinder wall to close their paths N-S. So most of the field lines will be in the metal cylinder wall between the N and S poles of the bar magnet; very little will get away from volume around the bar magnet, and very little should make it outside the cylinder as long as the flux density does not exceed the saturation flux density of the metal cylinder wall.

 

[Lotto]

If you have a bar magnet oriented along the hollow metal cylinder's axis, the field lines will use the cylinder wall to close their paths N-S. So most of the field lines will be in the metal cylinder wall between the N and S poles of the bar magnet; very little will get away from volume around the bar magnet, and very little should make it outside the cylinder as long as the flux density does not exceed the saturation flux density of the metal cylinder wall.

And if we have a magnetic flux at the end of the rod that is not zero, does it mean that the rod in not closed at the ends? How does then the field lines look like?

 

[berkeman]

And if we have a magnetic flux at the end of the rod that is not zero, does it mean that the rod in not closed at the ends? How does then the field lines look like?

For the bar magnet flux generated by the bar magnet inside the ferrous hollow cylinder, as long as the flux is not saturating the walls/ends of the hollow cylinder, if the ends are closed you should get no flux outside.

If one end of the bar magnet comes close to an open end of the hollow ferrous cylinder, then some of that flux will make it outside the end of the cylinder and loop back around to enter the outside wall of the cylinder and eventually make it back inside to the other pole of the bar magnet.

Helpful reference on flux lines from a bar magnet:

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html

 

[Lotto]

very little will get away from volume around the bar magnet, and very little should make it outside the cylinder as long as the flux density does not exceed the saturation flux density of the metal cylinder wall.

And for those lines outside the rod can we use the equation for the magnetic induction at the equator? I mean this $$B=\frac{\mu}{4\pi}\cdot \frac{M}{(r^2+l^2)^{\frac 32}}$$

 

[Vanadium 50]

It is easier to think in terms of energetics: you need to keep the number of field lines entering and exiting each pole the same. However, it will be hundreds of times cheaper to put a field line in iron than in air. So if you can move a line - or most of a line - from air to iron, that's what will happen.

 

[Lotto]

It is easier to think in terms of energetics: you need to keep the number of field lines entering and exiting each pole the same. However, it will be hundreds of times cheaper to put a field line in iron than in air. So if you can move a line - or most of a line - from air to iron, that's what will happen.

So if I understand well, the field lines will be in the rod, not outside in the air, so I can't use the equation above. Yes?

 

[Vanadium 50]

Very few will be in the air. I don't want to get into the details of "saturation" and "B vs. H curves", but in general, yes. If there's a path through the steel, the field line will take that rather than through the air.