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magnetic moment and magnetic flux，magnetic moment and residual magnetism
Magnetic Moment and Magnetic Flux
Magnetic moment can be converted from magnetic flux using the coil constant. Magnetic moment is an important parameter describing the magnetic strength of ferromagnetic materials, especially permanent magnet materials. Open-circuit magnetic moment is one of the factory qualification indicators for finished permanent magnets. The pull-out method is widely used in China’s permanent magnet industry to measure magnetic moment, and another important application of this method is the sampling inspection of the uniformity of large permanent magnets. Such testing is basically required for permanent magnets used in wind power generation and electric vehicles.
China has formulated GB 3217-2013, a standard for measuring the magnetic properties of permanent magnetic materials in closed magnetic circuits, but there is no corresponding standard for open-circuit magnetic moment measurement that meets the above requirements. At present, the existing international standard is IEC 60404-14 (Testing of magnetic dipole moment of ferromagnetic materials by pull-out or rotating method), and a similar standard is being developed in China.
By measuring an open-circuit sample in a Helmholtz coil with a strictly calibrated coil constant , the magnetic flux value can be obtained, from which the magnetic moment of the material can be calculated.
Calculation Formula for Measuring Magnet Magnetic Moment Using Fluxmeter and Helmholtz Coil
- = magnetic moment of the magnet, unit: Wb·cm⁻¹
- = coil constant, unit: cm⁻¹ (changes in the unit of the coil constant will result in changes in the unit of magnetic moment)
- = magnetic flux value, unit: Wb
Image source: Internet · Helmholtz Coil
It should be noted that during production and trading, it is very common to measure the magnetic moment of finished or specially shaped permanent magnets under open‑circuit conditions using the pull‑coil method. However, as most enterprises use self‑built measuring devices, measurement reproducibility is relatively poor due to factors such as coil calibration and operating techniques.
Calibration of the test coil requires applying a steady current in a zero‑magnetic‑field environment to measure the magnetic field intensity, thereby determining the coil constant. Nevertheless, genuine zero‑magnetic‑field laboratories are extremely rare worldwide, making the calibration of test coils difficult to popularize across the industry. Without proper calibration of the test coil, the accuracy and reliability of measurements will be directly compromised, which may further lead to trade disputes.
Magnetic Moment and Remanence
There is a functional relationship between magnetic moment and remanence, which is closely related to the dimensions of the magnet.
When the magnetic flux or magnetic moment of a magnet is known, if its shape and dimensions are given, the permeability coefficient of the permanent magnet material can be calculated, and then the values of , and of the magnet can be derived. Conversely, when the shape, dimensions and remanence are known, the magnetic moment of the magnet can be calculated.
(There is a typo in the formula below; the correct expression is .)
Pc: Permeance Coefficient
Permanent magnets operate under open‑circuit conditions. Since an open‑circuit magnet is subjected to a demagnetizing field, the magnetic induction intensity of the permanent magnet in its operating state does not lie at the point under closed‑circuit conditions, but at a certain point on the demagnetization curve lower than . This point is known as the operating point of the permanent magnet, such as Point D in the figure above.
The operating point depends on the shape of the demagnetization curve and the magnitude of the demagnetizing field acting on the magnet under operating conditions.
The straight line connecting the operating point D and the origin O is called the load line. Its slope is related to the demagnetization factor of the magnet and is also referred to as the permeance coefficient, denoted by .
The demagnetization factor is closely related to the geometry of the magnet. Therefore, the value of strongly depends on the shape and dimensions of the magnet.
More elongated magnets along the magnetization direction have a smaller demagnetization factor, while flatter magnets have a larger demagnetization factor, where or .
Note: Click the image to view a larger version. Please note that the Y-axis of the left graph represents -Pc.
The figure below shows the empirical formulas for estimating the permeance coefficient of NdFeB permanent magnets with different geometries, for reference only.
Once we understand the concept and calculation method of Pc, we can convert between remanence, magnetic moment and magnetic flux.
Given the dimensions and remanence of a sintered NdFeB magnet, how to calculate its magnetic moment and magnetic flux?
Note: Bdi refers to intrinsic flux density.
Recoil permeability μrec = Br / HcB (a commonly used estimated value for sintered NdFeB is 1.05).
Calculate the magnetic moment of the magnet inversely according to:
Bdi = magnetic moment / volume
According to the magnetic moment M = k * Ф, the magnetic flux Ф can be simulated and calculated when the coil constant k is determined.
*Source: WeChat Official Account – Zhao Magic Magnets (找磁材)