The force between a permanent magnet and soft iron pole piece

Problem statement

Consider a permanent magnet with a soft iron pole piece as shown in the sketch.

Extracted from the Part 1A Electromagnetics Handout 3 - Magnetic Materials.

Objective : to calculate the force per unit area f needed to just remove the pole piece from the magnet.
Principles : Ampere's Law, flux conservation and virtual work.

Method of analysis :	1)	Application of Ampere's Law and flux conservation. 
			2)	Energy balance method.

Sketch :

Maths :

Matlab(R) solution
Solution variables
Input variables



Mean length of magnet, lm (metres)		
Mean length of iron pole piece, li (metres)	
Relative permeablity of iron, mu_r 		
Field intensity Hm for this material		




Output variables



Magnetic Flux Density, Bm
Force per unit area, F/A