How to calculate magnetic braking force?

[dishwasher95]

TL;DR Summary

If a magnet is dropped through a copper tube, the magnet will travel slower towards the ground than if there was no tube at all. I understand the principle of why this is happening but I don't know how to calculate an exact value for the size of the braking force (in Newtons) that is acting upon the magnet as it falls through the copper tube. Is there a simple way of doing this?

I want to know how to calculate the braking force acting on a magnet falling through a copper tube.

The setup can be seen in this video (YouTube, @ 1:49 - 3:12): Copper's Surprising Reaction to Strong Magnets.

Note that it's not a copper tube in the video but a plastic tube surrounded by a copper wire (this doesn't matter as the same physical principles apply).

In the video, a magnet is dropped through a coil of copper wire, resulting in current going through the wire (when the circuit is closed) which generates a magnetic field opposing the magnetic field of the magnet falling through the coil.

How do I calculate the size of of the braking force? Or rather; how do I calculate the strength of the generated magnetic field in the coil?

Bonus question: Why does the magnet fall easily through the coil when the LED light is connected to the circuit?

I'm assuming it's because the resistance is increased in the circuit, meaning less current is passing through the coil, meaning a weaker opposing magnetic field is generated? Is this correct?

But then when the magnet is moving faster through the coil (where the LED is attached), shouldn't more voltage (EMF) be generated? Leading to more current?

Some equations that I have in mind:

Ohm's Law: V = R * I
(V = voltage [V], R = resistance [Ohm], I = current [A])

emf = B * v * l
(emf = electromotive force [V], B = strength of magnetic field [Tesla], v = relative velocity between magnetic field and copper wire [m/s], l = length of copper wire in the magnetic field [m])

Alright I think that's it - let me know if I should clarify anything.

Thanks!

 

[Baluncore]

How do I calculate the size of of the braking force? Or rather; how do I calculate the strength of the generated magnetic field in the coil?

To calculate accurate values requires an accurate model and a controlled orientation.

As the magnet falls, it's field cuts the conductive tube. A local voltage is induced proportional to the velocity of the magnet. That voltage causes an eddy current to flow in the copper, which opposes the falling magnetic field.

Ohms law relates the connection between resistivity of copper, induced voltage and eddy current.

Bonus question: Why does the magnet fall easily through the coil when the LED light is connected to the circuit?

The voltage drop across an LED before it conducts is a couple of volts. That is in series with the coil so it reduces the voltage induced, and so reduces the induced eddy currents.

 

[dishwasher95]

To calculate accurate values requires an accurate model and a controlled orientation.

As the magnet falls, it's field cuts the conductive tube. A local voltage is induced proportional to the velocity of the magnet. That voltage causes an eddy current to flow in the copper, which opposes the falling magnetic field.

Ohms law relates the connection between resistivity of copper, induced voltage and eddy current.

I'm sorry but this doesn't help me any further.
I need the equation. Is there an equation?

The voltage drop across an LED before it conducts is a couple of volts. That is in series with the coil so it reduces the voltage induced, and so reduces the induced eddy currents.

Could you elaborate?

Thanks!

 

[russ_watters]

The force is just the weight of the magnet; it is the velocity that is hard to calculate.

 

[dishwasher95]

The force is just the weight of the magnet; it is the velocity that is hard to calculate.

Can you elaborate? Maybe with a general equation?

Thanks!

 

[OmCheeto]

...

The setup can be seen in this video (YouTube, @ 1:49 - 3:12): Copper's Surprising Reaction to Strong Magnets.

...

Alright I think that's it - let me know if I should clarify anything.

Thanks!

Could you clarify the video address? It doesn't seem to be working.
I'm pretty sure I know what the video will show, but just wanted to make sure.

Also, the answer to your last question to Russ is: F = ma

Assuming of course, that the video shows what I think it shows.

 

[Baluncore]

I want to know how to calculate the braking force acting on a magnet falling through a copper tube.

I'm sorry but this doesn't help me any further.
I need the equation. Is there an equation?

Also, the answer to your last question to Russ is: F = ma

While the magnet is falling at a terminal velocity, the equilibrium counter force will be equal to the magnet mass, multiplied by the acceleration due to gravity.

The terminal velocity will occur when the rate of flux being cut is sufficient to counter that force across the gap between the unspecified magnet and the unspecified and distributed imperfect conductors nearby.

 

[dishwasher95]

Could you clarify the video address? It doesn't seem to be working.
I'm pretty sure I know what the video will show, but just wanted to make sure.

Also, the answer to your last question to Russ is: F = ma

Assuming of course, that the video shows what I think it shows.

Here's the direct link:

I'm not looking for how to calculate the gravity force acting on a mass.

I'm interested in calculating the breaking force acting on the falling magnet as it falls through the coil.

So to sum up: I need a general equation for the breaking force acting on the magnet as it falls through the coil.

Thanks!

 

[etotheipi]

Derivation of explicit braking force is given in this paper:
http://www.msc.univ-paris-diderot.fr/~phyexp/uploads/LaimantParesseux/Aimant-Tuyau2.pdf

It's easier to think about it in the rest frame of the magnet.

 

[Baluncore]

So to sum up: I need a general equation for the breaking force acting on the magnet as it falls through the coil.

That is the same as the weight of the magnet.
I think you actually want to calculate the velocity of the magnet at which the braking force is equal to the weight of the magnet. That is a more difficult problem.

 

[DaveE]

I'm not looking for how to calculate the gravity force acting on a mass.

I think you may have misunderstood why people are saying the force is just the weight of the magnet.

They are assuming "terminal velocity", i.e., the velocity is no longer increasing, so a=0 then F=0. the upward force of braking will equal the weight of the magnet. This doesn't really change your question though, you'll want to find force as a function of velocity.

 

[dishwasher95]

I think you may have misunderstood why people are saying the force is just the weight of the magnet.

They are assuming "terminal velocity", i.e., the velocity is no longer increasing, so a=0 then F=0. the upward force of braking will equal the weight of the magnet. This doesn't really change your question though, you'll want to find force as a function of velocity.

Yep! That's exactly what I need. An equation for braking force as a function of the magnets velocity.
Does anyone know what that looks like?

Thanks!

 

[DaveE]

I think this is an example of the sort of problem where you are better off learning the process to solve your specific problem, than getting "an equation". The problem is that that equation will depend on lots of different variables; things like the resistivity of the tube, every dimension (distance) you can think of, the properties of the magnetic field, etc.

 

[Baluncore]

As DaveE wrote...

As the magnet falls, it's particular field pattern cuts the copper tube. That induces an eddy current in the copper, which causes an almost equal, but opposite, magnetic field. Effectively a good inverted reflection of the magnets moving field.

The magnet will fall faster if the copper is further away and not coupled well to all the magnet's field.
The magnet will fall faster if the metal is less conductive, or thinner, and so a less perfect magnetic mirror.

The faster the magnet falls, the shallower will the currents be in a thick conductive wall, (due to skin effect). That thins the wall, increases the effective wall resistance, and so the magnet falls faster. That is a positive feedback.

So you have critical balances and orientation effects that cannot be calculated without a good Finite Element Model. A good model requires you know your magnet specifications, orientation and field geometry.

The best way to find the answer is to build a prototype and do the physical experiment.
FEM can then be calibrated and used to refine the design parameters.

 

[Dr.D]

Derivation of explicit braking force is given in this paper:
http://www.msc.univ-paris-diderot.fr/~phyexp/uploads/LaimantParesseux/Aimant-Tuyau2.pdf

It's easier to think about it in the rest frame of the magnet.

This paper is quite well done and gives both theoretical and experimental results. It is a good source to look at for a clear understanding.