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As the Biot-Savart-Law is based on experimentations in air, i like to know how to calculate the magnetic flux density in material with much greater permeability, where the circular like shape of the field distribution troughout the vicinity does not apply.

Does anyone has a hint where to find some further information or can answer the question directly?

The question relates to a a system of two magnetic coupled solenoid with a number of windings, where ferrite is used to improve the coupling and is based on a FEM-calculation.

Edit: The magnetic flux passes through both an air gap and the ferrite.

To interpret the solutions, i like to build up a better understanding for the results.

Thank you for any hints.