# Finding the resistive force of a magnet moving along coils

## Main Question or Discussion Point

Hi everyone!

I posted this in the ME section as well but thought this would be a good section as well. 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!
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BiGyElLoWhAt
Gold Member
I'm not sure how you set it up, but what's important to realize is that the emf is independant of the field. What it is dependant on, however, is the time rate of change of the field. The emf is generated so that the current induced by the voltage generates a field that opposes the change in field from your swinging magnet (I believe this is your setup?) The resistive force is then going to be dependant on the magnetic field and the magnetic dipole moment of the magnet.

Thank you for the response. I think I have figured it out using the equation f_mag= integral(I dL X B) (sorry I don't know how to type equations from my phone). Using faradays law this equation is then dependent on both the induced magnetic field and the magnet itself which is what I believe you are saying, correct? The time dependence also comes in through faradays law as well.

jim hardy
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2019 Award
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If there's no current through your coil i don't see how there'd be any force.
Your own formula has a current term, f_mag= integral(I dL X B)

So you have control over the force by how much resistance you place in series with the coil.
That is, if there's any voltage induced at all.
Intuitively it looks to me like,,
by symmetry, at opposite ends of the magnet you'd get equal and opposite induced voltages, resulting in zero net voltage. Only as the magnet nears the ends of the coil will you see voltage.

ahhh but you said in first paragraph "a coil", then in second paragraph "a system of coils" .

One experiment is worth a thousand expert opinions.....

Jim,

Thanks for the response. I apologize, it is a system of coils. I like your last line about opinions! Ultimately I will test a working model. Currently I have experimental data for the project minus the resistive force of the "generator". I plan on using the force in the damping term in the equation of a damped driven oscillator. This will allow for me to play with the variables in faradays law to see how best to maximize my design without overcoming my driving force. I know the resistive force is small but so is my driving force (vortex induced vibrations). Thanks for the response!

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jim hardy
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That's the best way, math plus empirical data.

I predict you'll find an optimum combination of nturns and damping resistor(s), maybe even with non uniform turns per inch out near the ends.

vortex.... i cant say that word without saying "shedding" ... sounds like fun.. ....

BiGyElLoWhAt
Gold Member
Just for my own clarification, when you say resistive force, do you mean the force of the induced magnetic field on the magnet going over the coils?

jim hardy