Electron magnetic replusion compared to coulomb attraction

1. Nov 16, 2012

zincshow

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. Nov 16, 2012

tris_d

I ditto that question. Why are you asking, what are you up to?

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

3. Nov 16, 2012

Staff: Mentor

Why would two electrons be attracted towards each other?

4. Nov 16, 2012

tris_d

5. Nov 16, 2012

Staff: Mentor

The OP specifically mentioned that the coloumb force was attracting them.

6. Nov 16, 2012

tris_d

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".

7. Nov 16, 2012

Staff: Mentor

I was going to assume so, but he also specifically placed both North poles towards each other.

8. Nov 16, 2012

zincshow

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.

9. Nov 16, 2012

tris_d

Interesting. I haven't noticed any of that, and I see now there is the same mistake in the title as well.

10. Nov 16, 2012

Staff: Mentor

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.

11. Nov 16, 2012

tris_d

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.

12. Nov 16, 2012

tris_d

Apart from QM I think chemistry and molecular dynamics have something to say about that as well.

13. Nov 16, 2012

Staff: Mentor

I don't see how, but ok.

14. Nov 16, 2012

tris_d

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.

15. Nov 17, 2012

Staff Emeritus
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.

16. Nov 17, 2012

tris_d

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.

17. Nov 17, 2012

tris_d

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.

18. Nov 17, 2012

DrZoidberg

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.

19. Nov 17, 2012

tris_d

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.

20. Nov 17, 2012

Staff Emeritus
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.

21. Nov 17, 2012

tris_d

I wish I was not stupid for math, but I get all we have to do now is figure out what is the actual value of 'a' and 'b' and we can calculate at what distance will magnetic attractive force overcome electric repulsive force. Can you help us work that out?

Mass: 9.109×10^−31 kilograms
Electric charge: −1.602×10^−19 coulombs
Magnetic moment: 1.001 bohr magnetons

What now? What equation do we use for magnetic moment and how do we fit "1.001 bohr magnetons" into it? Would this equation be the one to use here:

My math is really terrible, and I see lots of 'r' in that equation, but I have no idea how they cancel out. Are you saying that after cancellation that equation comes up as 1/r^4? Would that be incorrect then according to their statement that dipole magnetic moment drops off with the cube of the distance?

22. Nov 17, 2012

Staff: Mentor

You realize that in reality the magnetic force will never overcome the electric force right?

23. Nov 17, 2012

tris_d

How did you arrive to that conclusion? In z-pinch it happens when Lorentz force overcomes Coulomb force. And as for electron dipole magnetic moment, if you consider what Vanadium said it's just a matter of distance.

Did you see what I posted about Pauli exclusion principle? What else, what other force could it be that "stacks" electrons in the same orbit and aligns them to have opposite spin?

24. Nov 17, 2012

Staff: Mentor

We are talking about 2 particles, not a Z-Pinch.

Incorrect. Quantum mechanics tells us that this will not happen.

I wouldn't say the magnetic force does this, but it is a consequence of not being able to fall into a lower energy state with another electron unless this happens. The wavefunction of fermions interfere destructively when two fermions try to occupy the same state at the same time, and switching the spin means the two fermions are no longer in the same state.

25. Nov 17, 2012

tris_d

You said magnetic force will never overcome electric force, and I gave you an example where it happens. Lorentz force applies to 2 particles just as well as to many.

How many electrons do you imagine there needs to be for it to start working?

Where does it say so, what are you referring to? -- Are you trying to say Coulomb's law does not apply to two electrons or that this equation below does not apply to electron magnetic dipole moment?

Never mind.