Why a steel plate can shield magnetic field?

[w9537]

If I put a very long steel plate above a coil with DC, the magnetic field above the plate will decrease because of the shielding of the steel plate.

However, from the perspective of magnetci domain, some domains will be magnetized to turn to the direction of the magnetic field from the coil.

Therefore, the magnetic field above should be from two source. One of them is the coil, the other is the magnetic domain in the steel plate. As a result, the magnetic field should increase rather than decreasing. But in fact, the magnetic field will decrease.

This question has puzzled me for a long time. I hope someone could help me figure it out! Thanks!

 

[Dale]

Summary:: Since the magnetic domain in the steel plate will be aligned to the direction of the magnetization, they should contribute to the magnetic field above the plate. Why the steel plate can shield the magnetic field?

The magnetic domains align to the direction opposite the external magnetic field. Otherwise iron would be repelled from a magnet instead of attracted

 

[sysprog]

The magnetic domains align to the direction opposite the external magnetic field. Otherwise iron would be repelled from a magnet instead of attracted

oh no! all my cute fridge magnets! noooo!

 

[w9537]

The magnetic domains align to the direction opposite the external magnetic field. Otherwise iron would be repelled from a magnet instead of attracted

Thank you for the reply! It should be a subtraction.

Reply

 

[hutchphd]

The magnetic domains align to the direction opposite the external magnetic field. Otherwise iron would be repelled from a magnet instead of attracted

I do not believe that is correct. The magnetization of iron is parallel to the applied field.

Forces on the magnitized iron are dipole forces and couple to the field gradient.
The shielding is because the ferromagnet "grabs" all the available lines of flux and makes them internal

 

[w9537]

I do not believe that is correct. The magnetization of iron is parallel to the applied field.

Forces on the magnitized iron are dipole forces and couple to the field gradient.
The shielding is because the ferromagnet "grabs" all the available lines of flux and makes them internal

I used to understand the shielding effect by magnetic flux line. But the nature of this phenomenon is that the opposing magnetic field produced by the magnetic domain in the steel plate cancels the magnetic field produced by the coil.

 

[hutchphd]

How you choose to picture it is up to you, although I don't think it is a good one.. I am trying to correct some rather erroneous (or misleading to me at best) statements made previously.
The (linear) magnetization M of the iron is in the same direction as the field from the coil. It directly augments the field only inside the coil, although the geometry will alter the external field which provides the ill-named "shielding".
For AC fields the picture is quite different and shielding is an appropriate term.

 

[w9537]

How you choose to picture it is up to you, although I don't think it is a good one.. I am trying to correct some rather erroneous (or misleading to me at best) statements made previously.
The (linear) magnetization M of the iron is in the same direction as the field from the coil. It directly augments the field only inside the coil, although the geometry will alter the external field which provides the ill-named "shielding".
For AC fields the picture is quite different and shielding is an appropriate term.

Yes, I just find an explanation that seems plausible to me, and this explanation is better than magnetic-reluctance theory. If you can find a better version, please tell me! Thank you!

 

[hutchphd]

I don't know what a "better version" is. Presumably the version agreed upon by the general commmunity of physicists and taught to every undergrad as the "theory of e and m in materials" is a pretty well distilled essence. Your interpretation differs from this and I would recommend learning the conventional theory. Study Griffiths. The choice of course is yours.

I am still mystified by some of the previous explanations of the shielding.

 

[w9537]

I don't know what a "better version" is. Presumably the version agreed upon by the general commmunity of physicists and taught to every undergrad as the "theory of e and m in materials" is a pretty well distilled essence. Your interpretation differs from this and I would recommend learning the conventional theory. Study Griffiths. The choice of course is yours.

I am still mystified by some of the previous explanations of the shielding.

Yes, I know almost everything can be solved and calculated by Maxwell equations. What I want is to understand this intuitively like the interpretation in the book <Introduction to magnetic materials> by B. D. Cullity.

 

[vanhees71]

Hm, shouldn't one be able to calculate this for a simple geometry?

My suggestion is to use a spherical shell of finite thickness of some material with a magnetic permeability $\mu_r$ and calculate how the magnetic field looks given a magnetic field $\vec{B}_0=\text{const}$ at infinity. That should be easy to calculate using a magnetic potential $\psi$ with $\vec{H}=-\vec{\nabla} \psi$ (in SI units). Then all you need is $\vec{\nabla} \times \vec{H}=0$ (which is already fulfilled by the potential ansatz) and $\vec{\nabla} \cdot \vec{B}=0$, leading to the boundary conditions $\vec{H}_{\parallel}$ and $\vec{B}_{\perp}$ continuous at the boundaries of the shell and the constitutive relation $\vec{B}=\mu_r \mu_0 \vec{H}$ with ($\mu_r=1$ outside of the shell of course).

From the symmetry I think inside one has $\vec{B}=\text{const}$ and otherwise a dipole ansatz should do the rest.

 

[w9537]

Hm, shouldn't one be able to calculate this for a simple geometry?

My suggestion is to use a spherical shell of finite thickness of some material with a magnetic permeability $\mu_r$ and calculate how the magnetic field looks given a magnetic field $\vec{B}_0=\text{const}$ at infinity. That should be easy to calculate using a magnetic potential $\psi$ with $\vec{H}=-\vec{\nabla} \psi$ (in SI units). Then all you need is $\vec{\nabla} \times \vec{H}=0$ (which is already fulfilled by the potential ansatz) and $\vec{\nabla} \cdot \vec{B}=0$, leading to the boundary conditions $\vec{H}_{\parallel}$ and $\vec{B}_{\perp}$ continuous at the boundaries of the shell and the constitutive relation $\vec{B}=\mu_r \mu_0 \vec{H}$ with ($\mu_r=1$ outside of the shell of course).

From the symmetry I think inside one has $\vec{B}=\text{const}$ and otherwise a dipole ansatz should do the rest.

Yes, the magnetic field inside a spherical shell of finite thickness in a uniform field can be calculated as shown in the book <Classical Electrodynamics> by Jackson.

 

[vanhees71]

Great! That saves a lot of boring equation-solving to fit the boundary conditions ;-)).