## Measurement of Magnetic Flux/Moment and Anisotropic Axis with Helmholtz Coil

## As a most commonly inspected specification, the measurement method with Helmholtz coil is known as classic and straightforward and described in the standard IEC 60404-14.## some magnet users think it is sufficient with a report of BH curve to confirm the quality of each batch. However, in many cases it is far from enough. The measurement with Helmholtz Coil might be necessary: a motor producer would like to make sure the motivation force from each piece of segment well balanced to avoid vibration; a sensor producer can hardly accept a passive signal source with large deviations. |

### Magnetic Dipole

#### The Helmholtz coil method is based on the magnetic dipole theory, which means that the multipole-application is not in the scope of discussion. Therefore, the discussion in sequence will only on this dipole topic. In a microscopic view, the basic element of a magnetic dipole with moment *µ* is generated by a current of an electron which revolves around a nucleus, as shown in picture 1. On the other hand, the a magnetic dipole in free space has a well-defined field distribution as shown in picture 2.

Picture 1: electron revolving around a nucleus. |
Picture 2: field distribution of a magnetic moment. |

With a huge amount of such dipoles, a magnet, in a macroscopic view, shall have a similar property of dipole and its field distribution (it is similar but not equal, because there is a demagnetization effect relates the form of magnet.). And hence analogously to the electron, the dipole moment is given also as *µ*.

### Helmholtz Coil

#### Helmholtz coil provides a large region with uniform sensitivity. However, since the measurement is strictly based on the dipole distribution model, the installation of the coil and its vicinity shall be built with non-magnetic parts.

### Measurement of magnetic flux/moment

#### To setup the measurement device, the Helmholtz coil is connected to a fluxmeter. According to the standard IEC 60404-14, the magnet specimen is placed in the center of the coil so that the vector of moment is aligned with the coil axis. The drifting shall be at first compensated and then the fluxmeter is set to zero. By withdrawing the magnet from the coil, the reading on fluxmeter changes. Alternatively the magnet can be rotated by 180º so that the vector of the moment points in the opposite direction. If the rotation method is used, the reading must be divided by 2.

#### The magnetic dipole moment *µ* is proportional to the measured magnetic flux *Φ*,

*µ = kΦ*

#### where *k* is the Helmholtz coefficient of the coil. The calibration of *k* is very critical to determine the accuracy of measurement.

#### In practical, the measured moment is used to calculate the intrinsic working point in an open circuit *B*_{open circuit}, instead of Remanence *B*_{r}.

_{open circuit}

_{r}

*B*_{open circuit} = µ / V

_{open circuit}= µ / V

#### This measurement is easier and faster than the test of BH curve inspection. Since the *B*_{open circuit} is proportional to *B*_{r}, the magnet user can directly obtain the information of process distribution. Although an accurate *B*_{r} might be hard to be calculated, a calibrated sample product shall help the user to define the *B*_{open circuit} and its tolerance.

_{open circuit}

_{r}

_{r}

_{open circuit}

### Measurement of magnetic anisotropic axis

#### With the withdraw method and 3-axis-Helmholtz Coil, all three components of moment *µ*_{x}, *µ*_{y}, *µ*_{z} along X, Y, Z axis respectively are measured and interpreted into a deviation of the magnetic anisotropic axis. This measurement is currently no standard process, but in some cases are very useful for magnetic sensor industry. The deviation of anisotropic axis *α* is defined as:

_{x}

_{y}

_{z}

*α = arccos[(µ*_{x}^{2} + µ_{y}^{2}) / (µ_{x}^{2} + µ_{y}^{2} + µ_{z}^{2})]^{0.5}

_{x}

^{2}+ µ

_{y}

^{2}) / (µ

_{x}

^{2}+ µ

_{y}

^{2}+ µ

_{z}

^{2})]

^{0.5}