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Charles Link said:The magnetic moments experiencing a force to be drawn into the strongest region of the magnetic field which is at the center of the magnet (between the poles).
Charles Link said:They will also get pulled into regions of stronger magnetic field.
That's what the equation ## F=-\nabla U ## represents. There is a force whenever the potential energy ## U ## changes as a function of position. The magnetic moment being aligned with the magnetic field ## U=-\mu \cdot B ##) is a low energy state (when ## \theta =0 ## it minimizes ## U=-\mu B cos(\theta) ##), but the energy is even lower (more negative) when the magnetic moment moves to a region of stronger magnetic field ## B ##, thereby, it gets pulled into a region of stronger ## B ##. ## \\ ## Additional item: This is why I anticipate the best results for putting the center of the magnet just above the fluid level. If you put the magnet (considerably) below the fluid level, there would be as many magnetic moments being puled downward into the magnetic field as there are magnetic moments getting pulled upward into the field. The forces would then balance out with no change in the fluid level.Vibhor said:Hi Charles ,
Thanks for replying .
Why would a tiny bar magnet in a non uniform magnetic field move towards a region of stronger magnetic field ?
Charles Link said:Diamagnetism, as I know it, is a result that occurs because of free electrons in metals (such as copper and aluminum) that can move all over the material. The diamagnetism is the result of the motion of the charged particle (the electron) in the magnetic field,
That one comes as a surprise to me, but I can understand why it might occur. There is nothing energetically favorable in the diamagnetic case to have a magnetic field running through the material. In this case, apparently the system decides, (by LeChatlier's principle), that it doesn't want the introduction of the magnetic field and in this case minimizes its introduction by rotating to the smaller distance of traversal by the magnetic field. (The physics of diamagnetic materials can get very complicated, but if you think of it qualitatively as e.g. copper or aluminum where you have all kinds of free electrons, it might be reasonable to assume that the electrons will have a weak response away from the magnetic field.) These diamagnetic effects, (except for superconductors), are quite weak, and I believe any rotation that occurs will occur very slowly. These experiments with the diamagnetic and paramagnetic materials require well balanced samples and need to be free of things like air currents and breezes, etc. The string that they are suspended from needs to be quite fine, etc. ## \\ ## Perhaps someone else can also offer some additional insight... Diamagnetic materials is a subject to which I only have a brief introduction.Vibhor said:Could you please elaborate on the diamagnetic case as to why the rod becomes perpendicular to the field ?
As to why needle shaped diamagnetic substances orient differently than paramagnetic substances in magnetic fields, I found this description:
http://www.pa.msu.edu/people/stump/EM/chap9/Needles.pdf
Charles Link said:That's what the equation ## F=-\nabla U ## represents. There is a force whenever the potential energy ## U ## changes as a function of position. The magnetic moment being aligned with the magnetic field ## U=-\mu \cdot B ##) is a low energy state (when ## \theta =0 ## it minimizes ## U=-\mu B cos(\theta) ##), but the energy is even lower (more negative) when the magnetic moment moves to a region of stronger magnetic field ## B ##
I don't have a good explanation for it, but the effect is a very weak one. Even the screening of magnetic fields by diamagnetic materials, with the exception of superconductors is usually very weak. The best explanation I have follows from LeChatlier's principle, but it isn't conclusive. In any case, the effect you observe of the bar that turns at right angles to the field is likely to be a very weak one, so that it would take some very detailed calculations (calculations which I have not done), which take into account some second order and higher terms to explain the observed results. ## \\ ## The response of paramagnetic materials, and even ferromagnetic materials is more readily explained and the many of the calculations are rather straightforward. The calculations to quantitaively explain diamagnetic properties are in general much more detailed, and with the exception of superconducting materials, diamagnetic responses are normally very weak. ## \\ ## While we are on the subject of magnetism, one thing you might find of interest is this Insights article on magnetic surface currents that I authored. Below is a "link" to it. These calculations are of moderate or lesser difficulty, and give some interesting results. They are quite a lot simpler than most calculations I have seen to try to explain diamagnetic properties. https://www.physicsforums.com/insights/permanent-magnets-ferromagnetism-magnetic-surface-currents/Vibhor said:Could you please explain why does diamagnetic materials behave in opposite manner ( tendency to move towards weaker magnetic field ) ?
I don't know if this will help. In diamagnetic materials, the induced atomic magnetic moments are in the opposite direction of B. In paramagnetic materials, the magnetic moments tend to align in the same direction as B. A rough model of a magnetic moment is a current loop. So, for a nonuniform B field we get a picture as shown below.Vibhor said:Could you please explain why does diamagnetic materials behave in opposite manner ( tendency to move towards weaker magnetic field ) ?
@TSny I think this is quite helpful in explaining why the diamagnetic bar rotates to get as much material as possible away from the magnetic field. Thank you. A very satisfactory explanation. :) :) ## \\ ## And to quantify, the energy is ## U=-\mu \cdot B ##, but ## \mu ## is in the opposite direction of ## B ## in the diamagnetic material. (essentially the dot product becomes a minus sign because ## cos(180^o)=-1 ##). ## F=-\nabla U ## which will be opposite what is was for paramagnetic materials, where ## F ## was in the direction of increasing ## B ##. The paramagnetic material wants to have as much material in the magnetic path as possible, while the diamagnetic is the opposite. ## \\ ## One thing that is missing from this explanation though is why the diamagnetic material should generate a magnetic moment state that is energetically unfavorable by being aligned opposite to the applied ## B ## field, and thereby it becomes a state of higher energy... ## \\ ## And an additional note on diamagnetism, especially in metals: The De Haas-van Alphen effect, (which you can google), is an example of one type of diamagnetism, and a much detailed theory is required to quantify the effects. The diamagnetic susceptibility oscillates as a function of magnetic field strength, and thereby the explanation for it gets quite complex.TSny said:I don't know if this will help. In diamagnetic materials, the induced atomic magnetic moments are in the opposite direction of B. In paramagnetic materials, the magnetic moments tend to align in the same direction as B. A rough model of a magnetic moment is a current loop. So, for a nonuniform B field we get a picture as shown below.
View attachment 209380The B field is stronger below each loop. If you pick a point of the current loop, such as P in the diagram, you can see that B is not vertical. B has a horizontal component. If you use the right hand rule to determine the direction of the magnetic force on the current due to the horizontal component of B, then you find that the diamagnetic loop is pushed upward away from the strong field region. The paramagnetic loop is pulled downward toward the stronger field.
TSny said:I don't know if this will help. In diamagnetic materials, the induced atomic magnetic moments are in the opposite direction of B. In paramagnetic materials, the magnetic moments tend to align in the same direction as B. A rough model of a magnetic moment is a current loop. So, for a nonuniform B field we get a picture as shown below.
View attachment 209380The B field is stronger below each loop. If you pick a point of the current loop, such as P in the diagram, you can see that B is not vertical. B has a horizontal component. If you use the right hand rule to determine the direction of the magnetic force on the current due to the horizontal component of B, then you find that the diamagnetic loop is pushed upward away from the strong field region. The paramagnetic loop is pulled downward toward the stronger field.
A small magnet put between the magnetic poles will want to align itself so it has ## (+)...- +... (-) ##, where the parentheses are for the stationary magnet. if you got it very near the center, it might tend to stay there, but it is an unstable equilibrium point and is likely to finish up as ## (+)-+ ... ...(-) ## , or ## (+)... -+(-) ##, attaching itself to one pole or the other. ## \\ ## @Vibhor Your example with the small magnet is quite instructional in that it shows how the magnetic moment in the molecule of the paramagnetic material would respond. You should even be able to place it slightly below the center of the larger stationary magnet and see the upward pull that results. ## \\ ## You could perhaps even put a bunch of small magnets each inside a small plastic sphere and create a demo that would respond similarly to the liquid of your original post.Vibhor said:I think I agree with what you have said . I was actually thinking about the case where a bar magnet is brought close to the middle of a stationary bar magnet and whether the moving bar magnet feel any force .I tried to model the moving bar magnet as a magnetic dipole . I am not sure if you found my reasoning correct .
@TSny , what's your take on post#18 ?
Paramagnetic liquid is a type of liquid that contains atoms or molecules with unpaired electrons which can be influenced by a magnetic field.
Paramagnetic liquid rises in a magnetic field because the unpaired electrons in the liquid are attracted to the strong magnetic field. This creates a force that pulls the liquid upwards, causing it to rise.
The strength of the magnetic field directly affects the rise of paramagnetic liquid. The stronger the magnetic field, the stronger the force pulling the liquid upwards, resulting in a faster and higher rise. Conversely, a weaker magnetic field will result in a slower and lower rise.
Yes, there is a limit to how high paramagnetic liquid can rise in a magnetic field. This is because as the liquid rises, it becomes further away from the source of the magnetic field, causing the force to weaken and eventually balance out the gravitational force. Therefore, the liquid will stop rising at a certain height.
Yes, other liquids can also rise in a magnetic field. However, this phenomenon is more pronounced in paramagnetic liquids because of their higher number of unpaired electrons. Other liquids with a lower number of unpaired electrons, such as diamagnetic liquids, may also experience a rise, but it will be significantly weaker.