Finding resistive force from a magnet moved over coils

[Diesel17]

Hi everyone!

I am working on a thesis project and have a question for anyone who feels they can answer it. I am trying to find the resistive force created when a magnet moves along a coil of wire. I have put pictures below but here is the short explanation:

The pendulum, which is fixed at a point along the rod (D2 is about 2*D1 but that isn't important in this step) oscillates according to a driving frequency f . On top of the pivot is a magnet with the center drilled out. This magnet oscillates back and forth according to the pendulum's motion while moving over a system of coils. What I want to find is an equation for how much resistance is created as an emf is induced. I am having a hard time though because when I think about it conceptually I find the magnetic field to be in the same direction as the motion which would yield zero current. This isn't the case though so I am looking for some help setting this up.

For now I would like to leave the factors such as number of turns, field strength, etc as variables so that I can play with them and find which values will yield the best induced emf without completely ruining the motion as the driving frequency is fixed. Any ideas are greatly appreciated! I'm also new so if this is in the wrong section please just let me know!

 

[Randy Beikmann]

Just so you know, I'm not an expert in EM theory, but I have worked with electric motors. In particular, "induction motors" develop currents in their rotors by having the magnetic poles from the windings in the stator move along the stator faster than the rotor is turning. The changing magnetic field the rotor "sees" creates currents in the rotor, and the currents form electromagnets in the rotor.
So what's my point? The rate of change in magnetic field is what induces the currents in the rotor, not their relative direction. The exact laws in your case are different, but the back EMF you're interested in is only there when there is a relative velocity between the magnets - a rate of change of position. I think that's true whether the magnetic fields are in the same direction or not.

 

[Diesel17]

Thank you for the response. I believe I have figured it out. You are correct that the emf is produced my a change in the magnetic field (faraday's law). If the current is in the same direction as the field lines then the force is equal to zero which is proven by F=qV X B . I believe I found an acceptable answer by using

 

[Diesel17]

I'll try this again since my phone apparently wanted to submit that post before I finished typing...

I found an answer using a Halbach Array which allowed me to arrange the magnetic field in a way that is perpendicular to the induced current so the cross product is maximum. The resulting force is then perpendicular to my travel which would yield the expected damping force. Using a combo of faraday's law and the biot-savart law the resistive force f_mag can be found which is dependent on the magnetic field, the induced magnetic field, and time. If anyone else thinks of something or has a better way please let me know!