Hi, I was browsing through many academic papers and could find little information of a simple solenoid with a permanent magnet in the core of the solenoid. Solving the field in a simple solenoid is very straight forward, but I was having difficulty understanding the interaction between the permanent magnet and the solenoid - in terms of force. I would like to determine the force applied to the permanent magnet when the solenoid is energized. Please note that the permanent magnet is cylindrical, will always have some portion of itself in the core of the solenoid, and can move freely. Can anyone point me in the right direction or better yet show me how to develop such an equation? Please avoid giving me recommendations for FEM or similar tools. Thank you in advance!