# Compass and Magnetic Susceptibility

## Main Question or Discussion Point

Hi all,

I'm Luca from Italy.

This is the technical setting.

Assuming we have a compass/magnetometer placed on something of general shape and material.
The magnetometer feels the Earth's magnetic field that we call H_earth: we know, however, that the field measured by the magnetometer is NOT the true

H_earth, but:

H_measured = H_earth + H_induced + H_permanent

where

* H_induced represents the induced magnetic field perturbation attributable to magnetizable soft iron material in the environment where is the magnetometer

(the so called Soft Iron Effects);
* H_permanent represents the permanent magnetic field perturbation attributable to permanent magnetization (the so called Hard Iron Effects).

H_induced is variable in both direction and magnitude and is proportional to H_earth via the [3x3] susceptibility matrix K:

H_induced = K*H_earth.

H_permanent is fixed and constant relative to the magnetometer and its installation: a [3x1] vector.

Said that,

H_measured = H_earth + K*H_earth + H_permanent

NOW, to simulate a real scenario like that described above, with regards to the coefficients of the matrix K, I ask to you:

1) what can we say about K?
2) is it possible to simplify them?
3) could K be simmetric and/or what are the possible values of its coefficients, also in relation with the scalar value of Magnetic Susceptibility we read on literature?

To sum up: HOW can I build K on Matlab?

Thank you for you patience and for your help.

Regards,
Luca.