Lenz's Law & Eddy Currents: Questions

[foges]

Im doing an experiment in school about lenz's law, basically im getting a couple of copper tubes and dropping magnets down the copper tubes to see the velocity that the magnets slow down to. Now im hoping to get to terminal velocity within the copper tube. I have already ordered some mangets of www.supermagnete.ch (very strong magnets), but i dont know how long/thick/large in diameter, the copper tubes should be. My teacher suggested 1 meter?? does that sound about right?

Thanx a lot.

 

[CTho9305]

The diameter of the tubes should be pretty close to the size of the magnets. When I saw it demonstrated, cylindrical magnets about 1cm diameter were used, and the inner diameter of the tube was maybe 2mm more. I don't know how long the tubes will need to be to reach terminal velocity. 1 meter is enough to see the effect though.

 

[MrDudeMan]

if i were you, i would get probably 6-7 feet of tube, and cut a small hole in the side to start measuring the speed after it has been in the tube for a foot or so. it will be going faster at the beginning of the tube than it will at the end, so if you give it some time to slow down, you will get a more accurate reading.

 

[DrPizza]

Just go to a hardware store and get a section of 1/2 inch copper pipe. Works great.

I'm not positive, but I'm guessing that terminal velocity occurs in the first 30-40 centimeters with the magnets I've used in class. (neodymium magnets) It's a great demonstration because students mistakenly believe that just because the magnet is not attracted to copper that it has no effect on the copper.

 

[djhuber82]

The thickness of the copper pipe (wall thickness, not pipe diameter) will affect the speed. Thicker copper means lower resistance, which causes the eddy currents to be more effective at slowing the magnet. The easiest way to show this effect is to get a larger diameter pipe that fits over the inner pipe and then perform a drop with and without the outer pipe.

 

[foges]

 

[foges]

Ok, I just got all the equipment and have tested it out. it works great. im using 4, 5 & 6mm magnets and copper tubes with an inner diameter of .8, 1.3 & 1.5 mm, the thickness of the copper wire is constant.

For a 6mm x 9mm magnet to fall through a .8mm inner diameter copper tube (1m long), it took 18 seconds.

Does anyone know if the length of the magnet (or total mass) has any effect on the eddy currents created, because when i drop multiple magnets together down the tube, it goes very quickly, whilst if i have a smaller length of magnets it goes much slower. But if i have too few magnets, the magnets start spinning (because the diameter of the copper tube isnt small enough) and the fall goes faster.

 

[silverpig]

How do you get a 6mm magnet to fall down a .8mm tube?

 

[foges]

sry, meant 8mm 13mm and 15mm

 

[foges]

When dropping larger magnets down the copper tubes they go faster than when there are fewer. Is this because the copper tubes have reached their maximum potential of eddy currents?

Does anyone know any good websites on this topic?

 

[foges]

Ive been doing some research and i gather that maxwells equations should help me understand what happens in the copper tubes.

Im kind of stuck on how the equations work though, because i havnt done integration yet, only differentiation, can anyone help me on that?.

Ive found an upside down delta in his equations, what does that mean?

 

[JohnCU]

ehh i don't remember lenz's law? what equation is it?

edit: oh damn nevermind it was a simple one. seems like it was called something else in my book but anyway what are you trying to integrate? upside down delta can be a couple of diff things, curl, divergence or gradient.

 

[foges]

Lenz´s law is that:; "The induced current produced in the conductor always flows in such a direction that the magnetic field it produces will oppose the charge that is producing it."-Wikipedia

Maxwells equations can be found here:
http://en.wikipedia.org/wiki/Maxwell's_equations
It may not be what im looking for after all though.

I did the experiments yesterday and i got the results that as the inner diameter of the copper tube increases, the terminal velocity increases exponentially, and the rate (/second) at which it reaches terminal velocity is independent of the mass and length of the magnet. would this make sense?

 

[jackwhitter]

The rate it reaches terminal velocity is based on falling acceleration. gravity is constant.

i am assuming by inner diameter, you mean to make the copper tube larger and keep the magnets the same size? this creates a larger air gap, which decreases the magnetic field's effect and decreases the induced eddy currents. this air gap is inversely proportional by the square or the cube (don't remember the exact equation of the top of my head. but it is exponential)

the shorter magnet stops sooner because the eddy currents change direction faster. a longer magnet assembly creates a longer magnetic field along the copper tube. the shorter magnet completely changes the field direction faster as it moves down the tube. that is, when the top of the magnet travels the distance of the height of the magnet and reaches the point where the bottom of the magnet was when you started measuring the top point, then the magnetic field is now being reversed (sorry if this is confusing)! if you did tests, you would probably see a proportional relationship between the length of the magnet assembly and slowing distance.

 

[foges]

Thanx for the help.

Why do faster changing magnetic fields result a greater slowdown
When you say "changes direction", do you mean that when looking from the top of the tube, the field will go clockwise, then anticlockwise, etc...?

Would this be correct?:

According to Lenz?s Law; when a magnet passes a conducting material, that magnet will induce eddy currents into the conductor with a force that opposes the direction of the magnetic field created by the magnet. These forces aid to either slow down or completely stop the moving object.

 

[KF]

Originally posted by: foges

Why do faster changing magnetic fields result a greater slowdown

The current which flows in the conductor, which is the tube, is proportional to the rate of change of the magnetic field. This is what one of Maxwell's equations says. A greater current produces a stronger magnetic field opposing the magnets field.

 

[Born2bwire]

Originally posted by: foges
According to Lenz?s Law; when a magnet passes a conducting material, that magnet will induce eddy currents into the conductor with a force that opposes the direction of the magnetic field created by the magnet. These forces aid to either slow down or completely stop the moving object.

I do not like the way that is stated. The changing magnetic field induces eddy currents in a conducting media. The direction of the eddy currents is such that the resulting secondary magnetic field from the currents (a current loop is a magnetic dipole antenna) opposes the originally changing magnetic field. The secondary magnetic field then acts upon the magnet which is where the opposing force arises. The moving object cannot really stop due to the eddy currents. The eddy currents, as KF stated, are induced by a changing magnetic field. So as the magnet slows down, the eddy currents reduce. If the moving object would come to a complete stop, then that would be more of a result of other forces, like friction. One could probably show that in the limit case it would come to a complete stop if we are devoid of other forces but not in real life.