Eddy current pipe force equation

[robhlee]

When you drop a (strong) magnet into a copper pipe, it slows down. Is there an equation for calculating the force? I have searched and searched Google, but all i found was F=[(B^2)(l^2)v]/R, where B = magnetic field, l = circumference of tube, v = velocity of magnet, and R = resistance of pipe. I have plugged numbers in, but it does not seem to be reasonable!

I got the equation from: http://www.du.edu/~jcalvert/phys/eddy.htm

 

[cesiumfrog]

How did you know what value of B to use? Or of R, for that matter?

 

[robhlee]

B is the magnetic field strength of the magnet that is being dropped through the pipe. R is the resistance of the copper pipe; i just used the resistivity formula, taking into account the sheet form of the copper pipe (rolled out). Is that not common sense or am i missing something here?

 

[robhlee]

please someone help

 

[cesiumfrog]

Assuming the equation is correct, you presumably need to know the value of the magnetic field at the tube, which will be very weak compared to the field just in front of the magnet (this would be the most obvious possible mistake, if you just "plugged numbers in"). R will also be very small (not much resistance along the circumference of a solid metal tube). The equation is (more than linearly) sensitive to both of these values and you didn't say what was unreasonable about your result.

I suggest your experiments use the given equation for fall time (less opportunity for mistake). You'll need a (cheap) hall effect sensor (and battery, wire and multimeter) to roughly measure B, and perhaps a fancy integration (based on resistivity data) to confirm R. And you'll need more than one data point, if you wish to confirm the equation. At the very least, that means tubes of different circumference/thickness/composition. Or maybe you could drop battery-solenoids to vary B. Another problem is that the tube will conduct the magnetic flux, making it still harder to know B accurately.

 

[robhlee]

Cesiumfrog thanks for the replies, but you are wrong on one thing for certain...B is not weak because I'm using Neodymium magnets lol !
Seriously though, the walls of the pipe are pretty close to the magnet as it drops through.
Ill be more specific on the unreasonable data:

B = 1.06 T(typical Nd magnet)
L = .047 m (circumference of pipe and the length of current travel, effectively the "wire" i think)
v = .22 m/s (dropped 1 cm above the mouth of the tube -- v^2 = .5*a*x)
R = 0.0000325 ohm (using resistivity formula (copper's row value) taking into account "L")

...and the force comes out to be: 16.9 Newtons!

That's enough to hold approximately 1.7 kilograms (against gravity)! The magnet would not only be able to float, but shoot out back upward.

So, that is why I presume there the equation is incorrect, but I cannot find an equation on this subject anywhere else!

 

[robhlee]

btw the mass of said nd magnet is 13 g.

 

[cesiumfrog]

First, *where* in 3-space is 1.06T measured? (Compare to where in space the derivation involved "B".)

Second, if you drop the magnet from above, v may exceed terminal velocity, therefore you can*expect* initial force to be large (to slow the magnet down). This (questionable choice of v) is why I advised you instead use the other given formula (dependent on fall time period, rather than instantaneous velocity).

 

[robhlee]

I am not really sure about the Tesla measurement; if you don't mind can you elaborate on why this is important? (i am not doubting, just lost)

Ohhhhhhhh
i see
Thanks a lot cesiumfrog!

 

[SLG]

Copper does NOT conduct magnetic fields

Interesting Q/A. As a point of clarification, copper does not conduct magnetic fields. Only material with magnetic permeability such as iron, mu-metal, ferrite, etc. will conduct magnetic fields. The phenomenon under discussion is that eddy currents are generated in the copper tube because the permanent magnetic is moving which creates the currents. Stop the magnet, no current. Now the eddy currents that are created in the copper tube in turn create their own magnetic fields which oppose the magnetic fields from the magnet (Lenz's law), hence induce a repulsion force which slows the falling magnet.

Assuming the equation is correct, you presumably need to know the value of the magnetic field at the tube, which will be very weak compared to the field just in front of the magnet (this would be the most obvious possible mistake, if you just "plugged numbers in"). R will also be very small (not much resistance along the circumference of a solid metal tube). The equation is (more than linearly) sensitive to both of these values and you didn't say what was unreasonable about your result.

I suggest your experiments use the given equation for fall time (less opportunity for mistake). You'll need a (cheap) hall effect sensor (and battery, wire and multimeter) to roughly measure B, and perhaps a fancy integration (based on resistivity data) to confirm R. And you'll need more than one data point, if you wish to confirm the equation. At the very least, that means tubes of different circumference/thickness/composition. Or maybe you could drop battery-solenoids to vary B. Another problem is that the tube will conduct the magnetic flux, making it still harder to know B accurately.