Field due to Magnetic Materials

[physiguy]

Say you have a paramagnetic (or diamagnetic) sphere (or some other shape) and you apply a field of H = 10 Oe. Now, we have $H=(1/\mu)B-M$.

That would indicate that outside of the material, B and H are essentially the same, right? B = 10 Gauss, outside of the material.

But shouldn't the magnetization of the material affect the field outside, as well?

Certainly if these were permanent magnets it would. I would expect that in all cases we would want to integrate M over the volume of our shape, then calculate the field from that dipole moment. But these equations seem to suggest that would be zero. Or am I misunderstanding their terms?

Thanks!

 

[Meir Achuz]

The magnetization of the material affects both fields outside, but B and H are still equal.

 

[physiguy]

So let's say that I have a sphere (radius R) of permeability $\mu$ and I apply a field H = 10 Oe. Would it be correct to say that the field around the sphere is not uniformly 10 Oe, because the sphere changes its value? (And also correct that B = H?)

If so, what good is $H=(1/\mu_0)B-M$?

 

[physiguy]

Perhaps my question is not totally clear.

In H=(1/u)B-M, is H the applied field, or the total field, after the contributions of the magnetic material? And if it is the total field, how does this do us any good? I have always heard that H is what you "set on the dial."

 

[sardar]

Thank you for your question. The equations for magnetic fields in materials can be quite complex and can depend on the specific properties of the material. In the case of a paramagnetic or diamagnetic material, the magnetization (M) does indeed affect the magnetic field (B) outside of the material. However, the relationship between B and H is not always as simple as B=H+M. This equation is known as the magnetic susceptibility and it measures the degree to which a material can be magnetized in response to an external magnetic field.

In the case of a paramagnetic material, the magnetic susceptibility is positive, meaning that the material will become more magnetized in the same direction as the external field. This will result in an increase in the magnetic field outside of the material. On the other hand, in a diamagnetic material, the magnetic susceptibility is negative, meaning that the material will become less magnetized in the same direction as the external field. This will result in a decrease in the magnetic field outside of the material.

So in the case of a paramagnetic or diamagnetic sphere, the magnetization of the material will indeed affect the magnetic field outside of the material. The equation H=(1/\mu)B-M can be used to calculate the magnetic field inside the material, taking into account the magnetic susceptibility and the magnetization. However, for simplicity, we often assume that the magnetic field outside of the material is the same as the applied field (H), neglecting the effect of magnetization. This is a reasonable approximation as long as the material is not highly magnetized.

In the case of permanent magnets, the magnetization is significant and cannot be neglected. In this case, we would need to consider the dipole moment of the magnet and integrate the magnetization over the volume of the magnet to calculate the magnetic field outside. So your understanding is correct, the equations do suggest that the field outside of the material is zero, but this is only an approximation and the actual field will be affected by the magnetization of the material.

I hope this clarifies your understanding of the relationship between magnetic fields and magnetic materials. If you have any further questions, please don't hesitate to ask.