- #106
hutchphd
Science Advisor
Homework Helper
- 6,557
- 5,659
Is it long and thin or short and fat? If long and thin it looks like two monopoles I recommend that as a good start. This is not easy.
See the image in post #40. It looks like six N42 magnets and the loop is 2 or three times as big.hutchphd said:Is it long and thin or short and fat? If long and thin it looks like two monopoles I recommend that as a good start. This is not easy.
This refers to the question of how to get the change in flux over time which I think also has a few issues in this problem.Einstein44 said:Well that is the question. I am unsure of the correctness of this method, but I though it would be possible to approximate where the field lines first reach the coil, and then use this distance from + to - as it moves through the coil to take the time it takes to do so. Since then the component t is present in Faradays Law, I assumed this would solve the problem of the changing flux?
https://www.researchgate.net/publication/239035074_ELECTROMOTIVE_FORCE_Faraday's_law_of_induction_gets_free-falling_magnet_treatmentCharles Link said:Post 104 by @hutchphd makes me wonder if we are trying to do too much with it. The flux at the surface can be estimated to be ## \phi=\mu_o M A ##, and that will occur in approximately a ## \Delta z=.05 ## m distance. If the height it is dropped from is ## h=1.0 ##m, its speed will be about ## v= 4.5## m/sec. This makes for a ## \Delta t \approx .01 ## seconds. With ## \mu_o M=1.3 ##Tesla, and ## A=.0001 ## m^2, that makes for ## \mathcal{E} \approx +.01## volts, and then a corresponding pulse in the opposite direction as it passes out of the coil. If ## N=10 ##, that would make the voltages ##\pm .1## volts.
I understand @Einstein44 has some data. It would be interesting to see that?Charles Link said:and a follow-on: The voltage is proportional to the speed, but if it is dropped from a different height, ## \int V(t) \, dt ## for the positive or negative part of the pulse should remain the same. Perhaps the OP @Einstein44 should look at our latest estimates before he spends a lot of time on a lengthy computer program.
It seems to me that the flux inside the magnet is constant so the flux change contribution from the inside of the magnet is zero as the magnet cuts through the plane.Charles Link said:Scratch that=I see I goofed. Sorry.
Edit: One other problem I see now is we are computing the field outside the magnet, using their formulas, but we also need to treat the case where the material of the magnet crosses over the plane of the coil=we need to include the extra term. It's not real difficult to include this part, but it complicates the problem.
The magnetization ## M ## is assumed to be constant, but there is still an ## H ## from the poles that points opposite the ## M ##, and this ## H ## is not constant, but drops off in the center so that ## B ## is maximized there, so that ## \dot{B}=0 ## at the center. I believe the peak in the EMF is likely to occur shortly before the magnet crosses the plane of the coil, but we really could use some computer simulation results to verify our conjectures.bob012345 said:It seems to me that the flux inside the magnet is constant so the flux change contribution from the inside of the magnet is zero as the magnet cuts through the plane.
So would I have to create a special function for the induced emf depending on height? Does the time factor in the equation not solve this problem? I would rather like to solve this the proper mathematical way instead of making assumptions, since that would be too easy and not very accurate.Charles Link said:Post 104 by @hutchphd makes me wonder if we are trying to do too much with it. The flux at the surface can be estimated to be ## \phi=\mu_o M A ##, and that will occur in approximately a ## \Delta z=.05 ## m distance. If the height it is dropped from is ## h=1.0 ##m, its speed at the coil will be about ## v= 4.5## m/sec. This makes for a ## \Delta t \approx .01 ## seconds. With ## \mu_o M=1.3 ## Tesla, and ## A=.0001 ## m^2, (post 26 says ##d=15 ## mm, so we are within a factor of 2 here), that makes for ## \mathcal{E} \approx +.01## volts, and then a corresponding pulse in the opposite direction as it passes out of the coil. If ## N=10 ##, that would make the voltages ##\pm .1## volts.
I started to address this in post #108 but it probably needs more attention from others. As for making assumptions, that is a major part in solving difficult physics problems but if done thoughtfully it doesn't have to limit accuracy too much.Einstein44 said:So would I have to create a special function for the induced emf depending on height? Does the time factor in the equation not solve this problem? I would rather like to solve this the proper mathematical way instead of making assumptions, since that would be too easy and not very accurate.
Einstein44 said:I would rather like to solve this the proper mathematical way instead of making assumptions
Why is this problem important to you? Are you just curious or is it a project for something? Also, I think you mentioned earlier you already have some experimental data. Can we see that?Einstein44 said:I would rather like to solve this the proper mathematical way instead of making assumptions, since that would be too easy and not very accurate.
Not yet considering units I got a factor of ##2\pi## in front of the charge from the integration differential element ##2\pi \rho d\rho##. Also, if the origin is at zero, flux would get bigger as the charge moved through to the other side of the loop plane and away (from +##z## to -##z##). That can be handled by making it go as;hutchphd said:A slightly better result is to treat it as two monopoles. For a single monopole of strength ##q_m## at position z(t) the flux is just the solid angle subtended by the loop of radius R
$$flux=q_m(1-\frac z {\sqrt {z^2+R^2}})$$
The strength of each pole is as I obtained in #104 . Take some derivatives and put in z(t) or do it numerically. This will give a good physical result.
Edit: for S.I. probably need a ##1/4\pi## in that
In my coordinate system with ##z## positive up and the origin in the center of the coil, the positive charge is at ##z## and the negative charge is at ##z'##, the flux for both charges with ##z'## = ##z + L##; is;hutchphd said:Yes you need to flip the sense of the solid angle when going through the origin. And there should be a 2pi/4pi out front so for z>0 it should be I think $$flux=\frac {q_m} 2 (1-\frac z {\sqrt {z^2+R^2}})$$ with sign change for z<0. Thanks.
How exactly did you determine this equation? I couldn't find this anywhere so I assume you derived this one yourself ?Charles Link said:I think the remenance ## B_r ## could be an important value here. With ## B=\mu_o H +M ##, (if I'm not mistaken), it gives the value of the approximate ## M ## for the magnet. For N42 I see one data sheet that gives it as from 1.28 to 1.32 T. (See also post 2 of this thread by @berkeman ).
(Note: Sometimes the units are given with the formula ## B=\mu_o H+\mu_o M ##, so that care must be taken in using published formulas that involve ## M ##, to keep the units straight).
The experimental data that I collected was pretty inconsistent, since I think the magnets are moving through the coil too fast, leaving not enough time for the voltmeter to read it properly or something. I am still trying to find ways to improve this methodology, so unit I will have done so, I will collect all the data again and make it available to you.bob012345 said:Why is this problem important to you? Are you just curious or is it a project for something? Also, I think you mentioned earlier you already have some experimental data. Can we see that?
I think the answer to the EMF will therefore depend on the external load?Einstein44 said:So I am going to start from the beginning now:
My aim is to find the induced emf as a cylindrical N42 magnet falls through a coil of N loops.
To calculate this I use Faradays Law.
Now for that, I need to find the magnetic flux in the first place using the equation:
$$\phi =\oint BdAcos\theta$$
This is why I am now trying to find B for the magnet, in order to work out this problem.
I am attaching a picture below that might perhaps help with visualisation.
So yes, indeed involves a moving magnet.
Ok, thank you for your contribution. I will start off by doing the experiment and perhaps mention the theoretical way that this could be calculated (analytically).cmb said:As mentioned above, this is not a problem that is tractable by analytic equations and you should revert to a good 3D magnetics modelling package, as used for this sort of thing (designing solenoids and motors and such). In your case, I think just experimentation is the best means for you to deduce what you need to deduce.
Personally speaking, if this was just as a physics investigation for interest (... but it is your experiment and not sure on your desired end objectives ...) I would use an oscilloscope measuring across the open coil, then gradually add resistors.Einstein44 said:Ok, thank you for your contribution. I will start off by doing the experiment and perhaps mention the theoretical way that this could be calculated (analytically).
Since you're saying experimental is best and you seem to have done similar stuff, do you have any suggestions as to how I could make the experiment perhaps more accurate? Currently I am dropping the magnets through the coil of N loops using a tube to keep them at the correct angle, however I think that because they move so fast the voltmeter has some trouble with accurate readings.
Yes, the method with the tubes is something I already did to make the results more reliable, as of course the angle would vary the flux. I used paper instead, since it is hard to make plastic tubes for the right dimensions.cmb said:Personally speaking, if this was just as a physics investigation for interest (... but it is your experiment and not sure on your desired end objectives ...) I would use an oscilloscope measuring across the open coil, then gradually add resistors.
The shorter the coil I'd expect the higher the EMF impulse for a shorter time. The longer the coil, the lower the impulse but for longer. So coil length as well as turns is a factor.
If you wanted a longer pulse, try longer magnets (put a few of the same cylindrical types end to end). Does it make a difference? If you have 3 or 4 magnets, do you get more work out of them by spacing them out (with non magnetic in between)?
I would also use a plastic tube to drop them through, makes sense. I'd use PEX heating tubing because of its particular properties, and wind the coil straight on to that. (or nested tubes, if the magnet is much smaller than the coil a smaller tube to carry the magnet within a larger tube carrying the coil, will help align the magnet and keep its orientation less of a variable).
Let's hear back from you on some tabulated results! Happy experimenting!
The ## B=\mu_o H +M ## or ## B=\mu_o H+\mu_o M ## is fairly standard, (comes from the pole model of magnetism), but perhaps it is advanced E&M (electricity and magnetism). See J.D. Jackson Classical Electrodynamics. The remanence ## B_r ## as being the value of ## \mu_o M ## is something that comes out of deriving the magnetic field strength using the formulas. It is somewhat difficult to find good and simple write-ups of this stuff.Einstein44 said:How exactly did you determine this equation? I couldn't find this anywhere so I assume you derived this one yourself ?
You really need an oscilloscope for this, rather than a voltmeter. With just a voltmeter, you could get some good readings if you built a precision rectifier circuit, followed by an integrator circuit. Otherwise, with just a voltmeter, I think your experiment is very lacking, and your results can't be compared with any accuracy to the above theoretical calculations.Einstein44 said:The experimental data that I collected was pretty inconsistent, since I think the magnets are moving through the coil too fast, leaving not enough time for the voltmeter to read it properly or something. I am still trying to find ways to improve this methodology, so unit I will have done so, I will collect all the data again and make it available to you.
I have a suggestion for that. You can simulate doing the experiment on Mars or even the Moon!Einstein44 said:The experimental data that I collected was pretty inconsistent, since I think the magnets are moving through the coil too fast, leaving not enough time for the voltmeter to read it properly or something. I am still trying to find ways to improve this methodology, so unit I will have done so, I will collect all the data again and make it available to you.
This is basically meant for a longer project that I am doing. I honestly don't even have to do this, this is rather the way I would prefer to do It because I am curious and I like solving these kinds of problems mathematically, in order to learn more about the maths behind the physics, if you know what I mean.
Edit: I am open to suggestions for improving the experiment
Yes, that actually makes much more sense. I am going to see if I have one in the lab, or else I will simply get one. That way it would be much more easy to see what the actual voltage induced is at any point in time, e.g. in the middle of the coil. (which was one of the issues I had with the voltmeter)Charles Link said:You really need an oscilloscope for this, rather than a voltmeter. With just a voltmeter, you could get some good readings if you built a precision rectifier circuit, followed by an integrator circuit. Otherwise, with just a voltmeter, I think your experiment is very lacking, and your results can't be compared with any accuracy to the above theoretical calculations.
That makes sense. That wouldn't be too bad to be honest. I am going to see how much effort that will require, but I might actually do this. Also in combination with using an oscilloscope perhaps.bob012345 said:I have a suggestion for that. You can simulate doing the experiment on Mars or even the Moon!
There is an easy way to effectively lowering ##g## and that is set up a simple pulley and string holding the magnet with a counterweight something like this;.
View attachment 287537
By adjusting the ratio of the masses you can control the acceleration. For example, if ##m_1## is the magnet, letting ##m_2=\large \frac{m_1}{2}## gives an acceleration of ##\large \frac{g}{3}## like Mars and letting ##m_2 =\large \frac{5m_1}{7}## gives an acceleration of ##\large \frac{g}{6}## like the Moon.
Also, I recommend using fine wire for the loop since using fat wires makes it harder to know what the effective size ##R## of the loop actually is.
Yes, it could slow things down in a convenient way. One comment is the calculations are for a frictionless and massless pulley. I think you are likely to find in practice that it slows things down somewhat more than by the calculated value. Meanwhile, an oscilloscope should make for much better data.Einstein44 said:That makes sense. That wouldn't be too bad to be honest. I am going to see how much effort that will require, but I might actually do this. Also in combination with using an oscilloscope perhaps.
By all means, if an oscilloscope is available that would be much better.Charles Link said:Yes, it could slow things down in a convenient way. One comment is the calculations are for a frictionless and massless pulley. I think you are likely to find in practice that it slows things down somewhat more than by the calculated value. Meanwhile, an oscilloscope should make for much better data.
For completeness I should also point out that my outlined approximation should really include the "Dirac String" to connect the two "Dirac" monopoles. This would correspond to the body of the (thin) solenoid between the poles. I think it will look something likeCharles Link said:One additional comment: I think @bob012345 's post 123 is a very good one. That is almost exactly what I think you should expect to see with an oscilloscope trace. (The polarity might be reversed depending on which way you connect the leads to the oscilloscope).
It was particularly for this part of the magnet, when it crosses the plane of the coil, that I abandoned my attempt to simplify things in post 54. This approach that you @hutchphd introduced and @bob012345 applied in post 123 looks to me to be almost free of approximation. There is only two points ## z=0 ## and ## z=-L ## where the solenoid portion (i.e the extra ## \mu_o M ## term in ## B=\mu_o H +\mu_o M ##) will have a non-zero derivative. That seems to be erased in the mathematics, because, as has been pointed out, the flux from the poles, (i.e. the ## \mu_o H ## flux), is discontinuous at these points as well, but the derivatives are steady, and it looks like they do give the correct exact answer.hutchphd said:For completeness I should also point out that my outlined approximation should really include the "Dirac String" to connect the two "Dirac" monopoles. This would correspond to the body of the (thin) solenoid between the poles. I think it will look something like
$$flux _{solenoid string}=q_m\delta (x)\delta (y)[\theta(-z_2)-\theta(-z_1)]$$
where these are delta and step functions
It does not materially show up in the flux derivative I guess and it will not affect the approach or recession profile of the magnet flux.
I do rather like this cheap and dirty method...hope it works out well.
What exactly did you do to get this equation? No need to show your working, I am just wondering what you did. Perhaps I can derive this myself for fun.hutchphd said:A slightly better result is to treat it as two monopoles. For a single monopole of strength ##q_m## at position z(t) the flux is just the solid angle subtended by the loop of radius R
$$flux=q_m(1-\frac z {\sqrt {z^2+R^2}})$$
The strength of each pole is as I obtained in #104 . Take some derivatives and put in z(t) or do it numerically. This will give a good physical result.
Edit: for S.I. probably need a ##1/4\pi## in that