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

[tex]\nabla^2 A=-\mu J[/tex]

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.

 

[PJC01]

Your intuition is correct - the addition of an iron sphere into the solenoid will indeed affect the magnetic field strength and direction at the point where you calculated it using the Biot Savart law. This is because the Biot Savart law assumes that the medium through which the magnetic field is passing is vacuum, or has a constant permeability. When the permeability of the medium changes, such as when an iron object is introduced, the Biot Savart law is no longer applicable.

In order to accurately calculate the magnetic field in this scenario, you would need to take into account the magnetic properties of the iron sphere and incorporate them into your calculations. This can be done using the Ampere's law, which takes into account the magnetic permeability of the medium through which the field is passing.

In short, the Biot Savart law is only applicable in certain situations and cannot be used in a medium where the permeability changes. It is important to consider the properties of the medium when using any mathematical model or law in scientific calculations.