Basic question regarding magnetic fields

[TecHNooB]

When a magnetic field encounters a ferromagnetic material (think magnetic screening), the field essentially follows the material like an electric field would in a conductor. Why? I can see how applying a field may cause the little current loops to polarize such that the dipoles are aligned with the applied H field. I just don't see what causes the H field to be guided along bends.

The best explanation I could think of is that when an H field encounters a perfect conductor, it's supposed to move tangential to the surface of the conductor. Perhaps in imperfect conductors, H partially penetrates the conductor and continues to move according to this tangential behavior. This may also explain why H fields tends to leak a lot. It also suggests that the H field is stronger in the outside layer of a volume than in the inside. This does not explain what the dipoles are actually doing when an H field encounters a bend (it suggests they point in the direction of the bend, but not why they would do so).

Also, an ideal conductor would not have an H or E field. When we get an E field in a conductor, the E field obtained is almost transient in a way in that the conductor would rather have no E field and the resulting current is nature trying to balance E such that it is zero again. Is there such a parallel for H fields?

 

[Born2bwire]

Static magnetic fields are not affected by perfect conductors, they penetrate them with ease which is why magnetic shielding is a very difficult problem. In a ferromagnetic material, an applied magnetic field alines the dipoles in the ferromagnet. This enhances the field inside the material since the magnetic fields inside will essentially line up with the applied field. But since these are magnetic dipoles, there is a return field further out in space that flows opposite to the original applied field. Inside the material, all of the dipoles reinforce each other to enhance the field. But outside, the return path of these dipoles weakens the applied field. The net effect is that the applied field appears to be "guided" into the ferromagnet. In a way, it is guided because we find that the energy lost in the attenuation of the field outside the material is gained back by the enhancement of the field inside the material.

 

[TecHNooB]

Static magnetic fields are not affected by perfect conductors, they penetrate them with ease which is why magnetic shielding is a very difficult problem.

I didn't realize the H-field being zero within a conductor was only true for time-varying fields. I'll have to think about that one. Of course, you could explain it to me as well

Also, why do the fields bend around turns? Why does the field enter and leave in the same direction? What makes it leave in a shielding application versus being guided throughout the ferromagnetic material in an electromechanical application?

 

[Born2bwire]

I didn't realize the H-field being zero within a conductor was only true for time-varying fields. I'll have to think about that one. Of course, you could explain it to me as well

A perfect conductor only has an infinite loss associated with its permittivity, the boundary conditions for magnetic fields are only dependent upon the permeability. Permeability is generally unity for most materials with low loss.

 

[canis]

"Static magnetic fields are not affected by perfect conductors, they penetrate them with ease"

Not true.




"I didn't realize the H-field being zero within a conductor was only true for time-varying fields."

Depends on conductor and H field. Static H field does not preclude zero H field inside conductor.





"Also, why do the fields bend around turns? Why does the field enter and leave in the same direction? What makes it leave in a shielding application versus being guided throughout the ferromagnetic material in an electromechanical application?"

Flux and permeability.

 

[canis]

nm

 

[canis]

nm

 

[Born2bwire]

"Static magnetic fields are not affected by perfect conductors, they penetrate them with ease"

Not true.

Like I said before, the boundary conditions for magnetic fields are dependent upon the permeability of the material. A perfect conductor is a perfect electrical conductor. Its loss is represented by infinite conductivity but this does not affect its permeability, only its permittivity. As such, static magnetic fields are largely unaffected when we talk about such idealistic materials. In most of real life this is still true, few conductors have nonunity permeabilities. Copper, aluminum, silver and gold are common conductors that one would work with. The main exception being iron but iron is not commonly encountered as a conductor outside of its use in building materials.

Also, why do the fields bend around turns? Why does the field enter and leave in the same direction? What makes it leave in a shielding application versus being guided throughout the ferromagnetic material in an electromechanical application?

I missed this the first time, can you clarify what you mean? The shape of the field lines are dependent upon the source and the boundary conditions of the surrounding media. For magnetic fields, as far as we know there are only dipole sources. This means that no matter how small or basic the source is, the source is its own sink. That is, the field sources from the dipole and sinks back to a dipole. This is opposed to electric fields where the basic source is a monopole charge. The monopole is either a sink or source (this is why the divergence of a magnetic field is zero and the divergence of the electric field is related to the amount of charge).

In a shielding application, it is pretty much the same thing as a ferromagnetic material. That is, to shield from magnetic fields, we surround the desired shielded area with a thick shell of high-mu material. This causes incident fields to concentrate most of their energy in the high-mu material, leaving low amounts of fields penetrating through. Another way is to actively setup magnetic fields that oppose the incident fields (like placing a magnet in the back of a speaker to make it "magnetically shielded"). Again, this has to do strongly with the lack of monopole magnetic sources.

If you want clarification on how the ferromagnetic material behaves as a field enhancer inside and a field inhibitor outside, it may be best to look at a textbook like Griffiths, Purcell, or Grant & Phillips (I prefer Griffiths).

Basically what it comes down to is that we can represent the dipoles that exist in a ferromagnetic material as very tiny loop currents. If we align these loop currents using an applied magnetic field, the dipole moments line up and the loop currents also line up in a certain way. What happens is that you get antiparallel loop currents. That is, let's say we look at in 2D, the aligned dipole currents may look similar to this:

You will notice that on the interior, a loop current is cancelled out by its adjacent loops. That is, when the current points down, there is an adjacent loop element that points up. When we add it all up, we are only left with net currents that flow along the boundary of the material. These are called magnetic bound currents. So you see that the entire material acts like a big loop current, which creates a magnetic dipole field. So imagine then the dipole field, it is like two opposite D's. Inside the material, the direction of the magnetic bound current's magnetic field will be in the same direction as the applied field. But outside of the material, the fields from the bound currents must return (because it is a dipole after all), and so the fields loop around back, which means that a portion of the field is now anti-parallel to the applied field (if we assume a uniform applied field). This is how the cancellation occurs.

Classical electromagnetics follows linear superposition. So sometimes a good physical description can be arrived at by looking at the components that make up the total fields.

 

[canis]

"Static magnetic fields are not affected by perfect conductors, they penetrate them with ease"

"Like I said before, the boundary conditions for magnetic fields are dependent upon the permeability of the material. A perfect conductor is a perfect electrical conductor. Its loss is represented by infinite conductivity but this does not affect its permeability, only its permittivity. As such, static magnetic fields are largely unaffected when we talk about such idealistic materials. In most of real life this is still true, few conductors have nonunity permeabilities. Copper, aluminum, silver and gold are common conductors that one would work with. The main exception being iron but iron is not commonly encountered as a conductor outside of its use in building materials."


In a perfect conductor d(B)/d(t)=0. If a perfect conductor is introduced into a static magnetic field, the field will be warped around the conductor.

In addition it is observed in all known perfect conductors B=0 inside the conductor.

In theory and in known phenomenon, the assertion "Static magnetic fields are not affected by perfect conductors, they penetrate them with ease" is not true.

 

[canis]

d(B)/d(t) is the partial derivative in my above post. I used d for the partial symbol.