# Force on permanent magnet solenoid core

I was wondering, since a coil/solenoid will pull any ferromagnetic material inside it, does the initial magnetization of the object in question affect the magnitude or direction of the force? I know that the force will be $F=0.5I^2\frac{dL}{dx}$ where $L$ is inductance, $I$ is current and $x$ is distance, but it doesn't really tell me how it would change with a different initial magnetization. I'm pretty sure the rod would get saturated pretty fast either way if the current is strong enough.

tldr: Does a coil pull a magnetized steel rod harder than an unmagnetized one, and if it does, does it matter which pole is facing the coil?

Thank you!

• Where have you seen this equation? Right hand side of your equation has dimension of energy. – Azad May 15 '15 at 8:18
• Sorry noticed an error in it, it should be $frac{dL}{dx}$ i can't find the original webpage but this one has a very similiar equation (nr 2) jpier.org/PIERB/pierb37/14.11110508.pdf – maxx May 15 '15 at 8:25
• now it has dimension of momentum – Azad May 15 '15 at 8:32
• AAH/m=AA*(kgmm/(AAss))/m = kg*m/s^2=N, it is force. here is the original page info.ee.surrey.ac.uk/Workshop/advice/coils/force.html – maxx May 15 '15 at 8:36
• sorry my mistake – Azad May 15 '15 at 8:39

Assuming the unmagnetized one somehow become magnetized (eg because of ferromagnetism) it depends on the magnitude and direction of the magnetization vector of the magnetized one. Magnetic materials are composed of magnetic dipoles and the force felt by these dipoles is $F=\nabla(m\cdot B)$
• @maxx mutual inductance is dependent on the distance so you have $\partial M \over \partial x$. so I think yes. but not at the first moment. there needs to be a current and faraday's law creates that if it moves and the initial movement will be caused by the force I mentioned above. so in a sense it depends on the direction of initial magnetization indirectly. – Azad May 15 '15 at 8:53