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- FAQ
- Flux density

Table of Contents:

The magnetic flux density of a magnet is also called "B field" or "magnetic induction".
It is measured in tesla (SI unit) or gauss (10 000 gauss = 1 tesla).

A permanent magnet produces a B field in its core and in its external surroundings.
A B field strength with a direction can be attributed to each point within and outside of the magnet.
If you position a small compass needle in the B field of a magnet, it orients itself toward the field direction.
The justifying force is proportional to the strength of the B field.

There are no simple formulas that calculate this field for the various magnetic shapes.
Computer programs were developed for that purpose (see below).
There are simple formulas for less complex symmetrical geometries, which indicate the B field on a symmetry axis in north-south pole direction.
Subsequently, we are glad to share these with you.

\(\begin{align}B &= \frac{B_r}{\pi}\left[arctan\bigg(\frac{LW}{2z\sqrt{4z^2+L^2+W^2}}\bigg)- arctan\bigg(\frac{LW}{2(D+z)\sqrt{4(D+z)^2+L^2+W^2}}\bigg)\right]\end{align}\)

The unit of length can be selected arbitrarily, as long as it is the same for all lengths.

\(\begin{align}B &= \frac{B_r}{2}\left(\frac{D+z}{\sqrt{R^2+(D+z)^2}}-\frac{z}{\sqrt{R^2+z^2}}\right)\end{align}\)

The unit of length can be selected arbitrarily, as long as it is the same for all lengths.

Formula for the B field on the symmetry axis of an axially magnetised ring magnet:

\(\begin{align}B &= \frac{B_r}{2}\left[\frac{D+z}{\sqrt{R_a^2+(D+z)^2}}-\frac{z}{\sqrt{R_a^2+z^2}}-\left(\frac{D+z}{\sqrt{R_i^2+(D+z)^2}}-\frac{z}{\sqrt{R_i^2+z^2}}\right)\right]\end{align}\)

The unit of length can be selected arbitrarily, as long as it is the same for all lengths.

The formula for ring magnets shows that the B field for a ring magnet is composed of the field of a larger cylinder magnet with the radius *R*_{a}
minus the field of a smaller cylinder magnet with the radius *R*_{i}.

\(\begin{align}B &= B_r\frac{2}{3}\frac{R^3}{(R+z)^3}\end{align}\)

The unit of length can be selected arbitrarily, as long as it is the same for all lengths.

A free software that is limited to rotation-symmetric magnets is FEMM.

Just like other tools, FEMM calculates and charts only half of the magnet because the B fields are symmetrical.
The other half you have to imagine mirrored on the left.

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