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Hall Effect Measurement System

## What is a Helmholtz coil?

Helmholtz coil is a device that produces a uniform magnetic field over a small area. The Helmholtz coil is often used in physical experiments because of its open nature, which makes it easy to put or remove other instruments and make direct visual observations.

Features: wide space, easy to use; There is a good linear relationship between the magnetic field and the supply current. Using magnetic field space has a very wide uniform area; Suitable for the production of one- dimensional, two - dimensional, and three-dimensional magnetic field combinations.

**If you have a pair of identical current-carrying coils parallel to each other and coaxial, with current flowing in the same direction, the total magnetic field of the two current-carrying coils is uniform over a large area near the midpoint of the axis when the coil spacing is equal to the coil radius. Therefore, it has great practical value in production and scientific research and is often used as the measurement standard of weak magnetic fields. This pair of coils is called Helmholtz coils. The magnetic field distribution characteristic of the Helmholtz coil is that the magnetic field inside it is close to the uniform magnetic field, that is to say, the uniformity is relatively high, similar to the magnetic field of a long solenoid, but the uniformity is not as high. The uniformity can be increased by the arrangement of multiple groups of coils.**

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It is necessary to apply Bessel function or elliptic function and related techniques to calculate the exact magnetic field at any position in space. Along the central axis of the coil (z-axis), the calculation involved is relatively simple, and the magnetic field can be expanded as a z power series using Taylor expansion.

The rectangular coordinate system is adopted, and the center of helmholtz coil is taken as the origin O of z-axis. Since for symmetry in the XY - plane, the odd power must be equal to zero. By adjusting the distance H between the two coils, point O can be turned into an inflection point, so z2 level project can be guaranteed to be zero, so the leading uneven project is Z4 level project.