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Discuss Bill Compton's answer to: Dependence of an induced magnetic dipole on the field that induces it.

Can you show mathematically that diamagnetism alone exerts a repulsive force. Thus, diamagnetism can produce levitation. Note that a magnetic field induces a magnetic dipole with an opposite field to ...

Bill Compton Answered:

Your question can be divided into three parts which we shall discuss separately. However, the mathematical rationale is a bit complex, which your illustration fails to demonstrate.

The nature of diamagnetism. Note that the magnetic field is applied in one magnet and induced in another showing the same polarity, hence we have repulsion. We need to bring both into a superconductive state for the action to be significant: see the Meissner Effect.

The Lorentz Effect is wholly different from the Meissner Effect in that the Lorentz Effect operates at ninety degrees from the applied force and is sequential, hence we suffer specific related inefficiency of the Meissner Effect.

The Bose Effect is a paramagnetic vector that operates between the Lorentz Effect and Meissner Effect, rendering yet further inefficiency.

(Courtesy Wikipedia):

Theory of diamagnetism

The Bohr–van Leeuwen theorem proves that there cannot be any diamagnetism or paramagnetism in a purely classical system. Yet the classical theory for Langevin diamagnetism gives the same prediction as the quantum theory.[11] The classical theory is given below.

Langevin diamagnetism

The Langevin theory of diamagnetism applies to materials containing atoms with closed shells (see dielectrics). A field with intensity B, applied to an electron with charge e and mass m, gives rise to Larmor precession with frequency ? = eB / 2m. The number of revolutions per unit time is ? / 2?, so the current for an atom with Z electrons is (in SI units)[11]

$I = -\frac{Ze^2B}{4 \pi m}.$

The magnetic moment of a current loop is equal to the current times the area of the loop. Suppose the field is aligned with the z axis. The average loop area can be given as $\scriptstyle \pi\left\langle\rho^2\right\rangle$ , where $\scriptstyle \left\langle\rho^2\right\rangle$ is the mean square distance of the electrons perpendicular to the z axis. The magnetic moment is therefore

$\mu = -\frac{Ze^2B}{4 m}\langle\rho^2\rangle.$

If the distribution of charge is spherically symmetric, we can suppose that the distribution of x,y,z coordinates are independent and identically distributed. Then $\scriptstyle \left\langle x^2 \right\rangle \;=\; \left\langle y^2 \right\rangle \;=\; \left\langle z^2 \right\rangle \;=\; \frac{1}{3}\left\langle r^2 \right\rangle$ , where $\scriptstyle \left\langle r^2 \right\rangle$ is the mean square distance of the electrons from the nucleus. Therefore $\scriptstyle \left\langle \rho^2 \right\rangle \;=\; \left\langle x^2\right\rangle \;+\; \left\langle y^2 \right\rangle \;=\; \frac{2}{3}\left\langle r^2 \right\rangle$ . If $N$ is the number of atoms per unit volume, the diamagnetic susceptibility is

$\chi = \frac{\mu_0 N \mu}{B} = -\frac{\mu_0 N Z e^2}{6 m}\langle r^2\rangle.$

Posted 1 year ago
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Guard, protect and cherish your land, for there is no afterlife for a place that started out as Heaven. Charles M. Russell, Montana, 1929.

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Anonymous Comment

Rocmike in the last 13 hours you have posted under your aliases Bill 5 hours, Dr. Kelly 4 hours, Harley Spirit, 2 hours, Anselmox 3 hours and still posting. You also had posts with Fletcher and anonymous. All posting exactly the same and repeating the same crap over and over and using the word Atheist. Rocmike You need help not to mention a life.

Anonymous Comment

Rocmike this is a public website. You know no more about being a scientist then your other aliases know about being a doctor, lawyer, biker, engineer, model, chemist, model a black man or what ever else you pretend to be in your insane sick mind. Rocmike why do all of your aliases claim I am a woman? Can you make it any more obvious they are are all coming from the same poster.

Bill Compton

Paul, let's review. Note the Feynman diagram I sent you on photoelectron development in dissimilar metals, particularly Ge-/Si++ with epitaxial GaAsP bombarded with monochromatic photoelectrons. Note also that we have applied an epitaxial layer of SiN(3) to the opposite side of the wafer.

This material is used far more commonly than you believe. I was with TML during the R&D phase. It is now in use worldwide as a nanovolt transducer.

Anonymous Comment

Rocmike all i see is you googled somethng then copy and past it.

Anonymous Comment

Rocmike Bill, Anselmox and Paul Wittenberg are your aliases. You need help.

Comendore

Why do you have two profiles Bill? Who is this Bill in the complements section with no profile?

Njoy's Activity on AOL Answers.

http://aolanswers.com/people/3506981119864

Anonymous Comment

Rocmike you have posted the last 9 straight hours ,4 hours under your 2 Bill aliases profiles and 5 straight hours under the Actual Paul Wittenberg. You have also posted under anonymous and another Paul Wittenberg. Why do you have 2 profiles for Bill and Paul? With all the aliases you have are you running out of names? This also doesn't count the hours upon hours you have put in the last 24-48-72 hours. You do nothing but repeat the same thing over and over. You need help and a life. I just found another Alias that Rocmike has been posting under in the last 9 hours, Top Renner.

Bill Compton

Anselmo, I agree with you about magnetic separator systems currently in use at landfills. If we are to clean up the planet we must allow scientists to address problems that leftist politicians forbade us to address in decades past.

Anonymous Comment

Rocmike under your Bill alias alone you are on AOL 3 to 7 hours a day.

Anonymous Comment

Rocmike aka American Patriot you have been stealing peoples monikers and posting under them for a long time. You have also used your own aliases monikers and claimed someone stole them to take the heat off of you. Once a loser always a loser. You stole froggies moniker.