Can the Biot Savart law be used in a medium where the permeability changes?

[jim4444]

Say I use the Biot Savart law to calculate the magnetic field strength at a single point somewhere inside solenoid. I record this value. Then I add an iron sphere to the inside my solenoid very close to but not touching the point just calcuated. If I were to recalcuate the field strength at this same point I will get the same value as before because the iron is not included in the integration. Intutivaly this will not be correct because the iron will effect the field strength and direction in the air around it. What am I missing here ? Is it that I we not use the Biot Savart law in a medium where the permittivity changes ?

 

[Mbert]

I think that since Biot-Savart comes from the solution of Poisson's equation (with some curl of A and some manipulations), the permeability has to be uniform. This is how you get Poisson's equation in magnetostatics

$$\nabla^2 A=-\mu J$$

M.

 

[Gordianus]

The Biot-Savart law gives the B field in vacuo or in a medium of uniform permeability. Your example has two parts: air (or vacuum) and iron. Hence, you shouldn't use the Biot-Savart law.

 

[jim4444]

That is what I suspected. Thanks for the info.