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Electron magnetic replusion compared to coulomb attraction

  1. Nov 16, 2012 #1
    I know that the electron has an electric charge of 1.6x10^-19C and a magnetic moment of 9.3x10-24J/T. If you placed two electrons 1 angstrom apart in such a way as their north poles are pointing at each other, the coulomb force would attract them and the magnetic force would repel them. Which would win out?

    I know how to calculate the force on the electrons based on the coulomb force, but I do not know how to calculate the force on the electrons based on the magnetic force. Does anyone know how to calculate the magnetic force of repulsion on two stationary magnets? or have a suggestion of a web site that tells you how to calculate the force of repulsion on two stationary magnets?
     
  2. jcsd
  3. Nov 16, 2012 #2
    I ditto that question. Why are you asking, what are you up to?

    Here is my thread about something similar:
    https://www.physicsforums.com/showthread.php?t=648966


    http://en.wikipedia.org/wiki/Magnetic_dipole_moment

    87ee5b0ca7607534ce921bb60738a13c.png
     
  4. Nov 16, 2012 #3

    Drakkith

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    Why would two electrons be attracted towards each other?
     
  5. Nov 16, 2012 #4
  6. Nov 16, 2012 #5

    Drakkith

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    The OP specifically mentioned that the coloumb force was attracting them.
     
  7. Nov 16, 2012 #6
    Lapsus calami. It can't be the other way around, so he must have meant: "the coulomb force would repel them and the magnetic force would attract them".
     
  8. Nov 16, 2012 #7

    Drakkith

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    I was going to assume so, but he also specifically placed both North poles towards each other.
     
  9. Nov 16, 2012 #8
    Sorry, poorly worded and not checked. Better: 2 electrons 1 angstrom apart repelling each other through the coulomb force, but attracting each other through the magnetic force -or- 2 electrons 1 angstrom apart attracted by a proton inbetween them, hence the proton is attracting them and the electrons are repelling each other ... I was after the magnetic force calculation and clearly did not give enough thought to my layout. Darn ...

    tris_d: Thanks, I had not seen that page, it will take a while to digest it.

    The main question: at short distance which is the stronger force for an electron, the coulomb force or the magnetic force? Do they compare or is one "much" bigger then the other? Is the magnetic force an insignificant force at very small distances compared to the coulomb force?

    Also: I have recently found this page http://www.kjmagnetics.com/calculator.asp, but I am not sure it helps me. I am looking for a formula I can punch in the distance apart and compare the coulomb force to the magnetic force for 2 electrons.
     
  10. Nov 16, 2012 #9
    Interesting. I haven't noticed any of that, and I see now there is the same mistake in the title as well.
     
  11. Nov 16, 2012 #10

    Drakkith

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    I believe the coloumb force is far stronger than the magnetic force. But at this scale and distance Quantum Mechanical phenomena become dominant, so it may not be easy to explain.
     
  12. Nov 16, 2012 #11
    That I want to know too. Have no idea how to work it out.


    Formula I posted above takes mass and distance and gives you the force. The strange thing is I think that equation looked differently on that Wikipedia page few years ago. I think dipole magnetic moment should fall off with the cube of the distance, not square.
     
  13. Nov 16, 2012 #12
    Apart from QM I think chemistry and molecular dynamics have something to say about that as well.
     
  14. Nov 16, 2012 #13

    Drakkith

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    I don't see how, but ok.
     
  15. Nov 16, 2012 #14
    It just rings me a bell, probably due to molecular electric dipoles, but then there are molecular dynamics equations based on QM, so if that magnetic dipole moment of electron has some impact greater then insignificant it could be a part of some of those equations.
     
  16. Nov 17, 2012 #15

    Vanadium 50

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    The force you wrote above goes as 1/r4 and the Coulomb force goes as 1/r2. So classically, there is a region where the magnetic force is stronger. Quantum mechanically, there is not.
     
  17. Nov 17, 2012 #16
    Ok, I found it now where I got that thought from.

    http://en.wikipedia.org/wiki/Pauli_exclusion_principle
    - The Pauli exclusion principle helps explain a wide variety of physical phenomena. One particularly important consequence of the principle is the elaborate electron shell structure of atoms and the way atoms share electrons, explaining the variety of chemical elements and their chemical combinations. An electrically neutral atom contains bound electrons equal in number to the protons in the nucleus. Electrons, being fermions, cannot occupy the same quantum state, so electrons have to "stack" within an atom, i.e. have different spins while at the same place.

    - An example is the neutral helium atom, which has two bound electrons, both of which can occupy the lowest-energy (1s) states by acquiring opposite spin; as spin is part of the quantum state of the electron, the two electrons are in different quantum states and do not violate the Pauli principle.


    It seems to me Pauli exclusion principle describes the same thing as in the question from opening post, where two electrons would pair up by having their opposite magnetic poles turned towards each other.
     
  18. Nov 17, 2012 #17
    Can you explain that a bit more, with some example and actual numbers?


    By the way, don't you mean 1/r^3 instead of 1/r^4? It says here:

    http://en.wikipedia.org/wiki/Magnetic_dipole_moment
    The dipole component of an object's magnetic field is symmetric about the direction of its magnetic dipole moment, and decreases as the inverse cube of the distance from the object.
     
  19. Nov 17, 2012 #18
    Classically, if you model an electron as a spinning electrically charged sphere with a radius > 0, i think it would have to spin faster than the speed of light for there to be a region where the attraction is stronger than the repulsion.
     
  20. Nov 17, 2012 #19
    They have no size, being point particles, so spin rate is not really defined. And it's not important, we just say that magnetic dipole moment is INTRINSIC property of an electron and we are only concerned by the force produced due to interaction of those magnetic fields compared to force between electric fields.
     
  21. Nov 17, 2012 #20

    Vanadium 50

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    If the electric force is 8/r^2 and the magnetic force is 2/r^4, at r < 0.5, the magnetic force is stronger. If the electric force is a/r^2 and the magnetic force is b/r^4, at r < sqrt(b/a) , the magnetic force is stronger. So there is always a line where the Classical magnetic force is stronger.

    Read what I wrote. I said "the force you wrote above". I didn't check to see that it is correct or not.
     
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