Magnetic Flux Density (B)
When a ferromagnetic or ferrimagnetic material is placed in an external magnetic field, its atomic magnetic moments tend to align with the applied field. This alignment creates an additional internal magnetic field, known as magnetization (M). The combined effect of the external magnetic field (H) and the magnetization (M) inside the material results in what we call magnetic flux density, symbolized as \(B\).
In simple terms:
\(B\) = The total magnetic field that the magnet actually experiences.
In a vacuum, magnetic flux density is proportional to the external magnetic field:
\[ B=\mu_0 H \]
where \( \mu_0=4 \pi \times 10^{-7} H/m \) is the permeability of free space.
Inside a magnet or magnetic material, the formula becomes:
\[ B= \mu_0(H+M) \]
The unit of \(B\) is Tesla (T).
In the CGS system, the unit is Gauss (Gs), where \(1 T=10,000 Gs\).
Magnetic Polarization (J)
From the formula:
\[ B= \mu_0H+ \mu_0M \]
The term \( \mu_0M \) is defined as magnetic polarization, represented by \(J\):
\[J= \mu_0M \]
\(J\) also uses Tesla (T) as its unit.
- Physically, \(J\) corresponds to the magnetic dipole moment per unit volume inside the material.
- It is sometimes referred to as internal flux density.
In soft magnetic materials, the external field HHH is usually small (generally < 1000 A/m), so the difference between \(B\) and \(J\) is minimal.
However, in hard magnetic materials (such as NdFeB), magnetization is strong and stable, so the difference between \(B\) and \(J\) becomes large.
Therefore, both B-H curves and J-H curves are typically provided when analyzing permanent magnets.
This diagram shows the B–H and J–H curves of a permanent magnet.
- Br represents the remanence, the magnetism retained after the external field is removed.
- HcB and HcJ indicate how resistant the magnet is to demagnetization.
- Js is the maximum magnetic polarization the magnet can reach when fully saturated.
The curve in the second quadrant is the commonly used demagnetization curve, which is critical for evaluating magnet performance in real applications.
In the graph above, the second quadrant represents the demagnetization curve, which is the one we commonly refer to when discussing permanent magnet performance.