# Magnetic moment and flux, magnetic moment and remanence

In the last issue, yueci introduced the source of magnetism and the concept of atomic magnetic moment from the microscopic level. We know that everything in the universe is magnetic. Magnetism mainly originates from atomic magnetism. We can use magnetization, m ~ H curve and susceptibility to describe the magnetic properties of matter. In this issue, we will introduce the relationship between magnetic moment and flux, remanence, and how to measure or calculate the magnetic moment of magnet.

## Magnetic moment and flux: can be converted by coil constant

Magnetic moment is an important parameter to describe the magnetic strength of ferromagnetic materials, especially permanent magnet materials, It is very common for domestic permanent magnet industry to measure magnetic moment by pulling method. Another important purpose of measuring magnetic moment by using this method is to sample and inspect the uniformity of large permanent magnets. The permanent magnets for wind power generation and electric vehicles basically need to be tested. China has formulated the standard gb3217-2013 for measuring the closed magnetic circuit magnetism of permanent magnet materials, but there is no relevant method standard for measuring the open magnetic moment applicable to the above requirements. At present, the existing international standard is iec60404-14 (pulling or rotating method for measuring the magnetic dipole moment of ferromagnetic materials), and similar standards have been formulated in China.
The open circuit sample can be measured in the Helmholtz coil with strictly calibrated coil constant K, and the magnetic moment M of the material can be calculated by the magnetic flux value.
The calculation formula for measuring the magnetic moment of magnet by fluxmeter and Helmholtz coil is as follows:

M = k*Ф
• M is the magnetic moment of the magnet, in Wb·cm-1
• K is the coil constant, in cm-1
• Ф is the value of magnetic flux, unit: WB The picture comes from the network · Helmholtz coil

It should be noted that in the process of production and trading, it is very common to measure the magnetic moment of finished products or permanent magnets with special shapes by pulling coils under open circuit. However, the measurement repeatability of the measuring devices built by general enterprises is poor due to the influence of coil calibration, operation methods and other factors.
The calibration of the test coil requires a constant current to test the magnetic field under zero magnetic field environment, and then the constant of the test coil can be obtained. However, there are only a few zero magnetic field laboratories in the world, so the calibration of test coil is difficult to promote in the industry. The lack of calibration of test coil will directly affect the accuracy and reliability of the test, and may bring some trade disputes.

## Magnetic moment and remanence: it has a function relationship and is closely related to the size of the magnet

If the shape and size of the magnet are known, the values of Br, HcB and (BH)max of the magnet can be obtained by calculating the permeabilities PC of the permanent magnet material, and vice versa, if the shape, size and remanence of the magnet are known.

## Permeability coefficient Pc

The permanent magnet works in the open circuit state. Because the magnet in the open circuit state is under the action of demagnetization, the magnetic induction intensity of the permanent magnet in the working state is not at the br point of the closed circuit state, but at a point on the demagnetization curve lower than Br, which is called the working point of the permanent magnet.
The working point is related to the shape of demagnetization curve and the demagnetization field of the magnet. The line connecting the working point D and the origin o is called the load line. Its slope is related to the demagnetization factor of the magnet. The slope of the load line is also called the permeability, which is expressed by PC.
Pc=BD/ H=μ0(1-1/Nor Pc=1-4π/N
The demagnetization factor is closely related to the geometry of the magnet, so the Pc value is closely related to the shape and size of the magnet. The longer the magnetization direction, the smaller the demagnetization factor, and the flatter the magnetization, the greater the demagnetization factor, 0<N<1 or 0<N<4π.

The figure below is the calculation formula for calculating the Pc of NdFeB permanent magnets of different shapes found on the Internet by yueci for your reference (different types of magnets have different Pc calculation methods, and the following formula is only applicable to sintered NdFeB). Source: China Permanent Magnet Manufacturer – www.ymagnet.com              