An electromagnet attached to a soft iron pole piece

Problem statement

Consider an electromagnet with a core of permeablity mu_r wound on coil of n turns carrying a current I. A pole piece made of identical material is placed across the poles of the magnet 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



Relative permeability, mu_r 				
Mean length of electomagnet and pole piece, l (metres)	
Number of turns on coil, n 				
Current through coil, I (Amperes)			




Output variables



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