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Magnetic energy density

  1. Oct 29, 2015 #1
    1. The problem statement, all variables and given/known data
    In an atom: suppose one electron orbits the n proton nucleus at radius r . Find the magnetic energy density, in J/m3, at the center of the atom due to the motion of this electron.

    NOTE: You can ignore the effect of other electrons in this atom.

    2. Relevant equations
    u=B^2/2*u_o
    = (N*u_o*I)^2 /2u_o
    or=N*(u_o*I)^2 /2u_o
    3. The attempt at a solution
    1)
    Is the number of protons can be treat as the number of turns of the magnetic field, should I plug N inside the parentheses

    2)
    Since qvB=IBL and I get I=qv/L, and then I use mv^2/r = kqq/r^2 to get the expression of v and plug it in qv/L and finally plug the expression of I in the (N*u_o*I)^2 /2u_o.
    Am I on the right track or it is completely wrong?
     
  2. jcsd
  3. Oct 30, 2015 #2

    rude man

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    I am not sure what you were trying to do. Looks like you are trying to use Ampere's law but this is not applicable here.
    I suggest:
    1. find B at the center of the atom. This involves finding the speed of the rotating electron as it circles around the N-proton nucleus. You now have a curren loop of known parameters (i and r) centered on the nucleus.
    2. Use Biot-Savart (or your textbook, probably) to determine B at the nucleus.
    3. Use your formula for energy density.
     
  4. Oct 30, 2015 #3
    Thank you for the reply. And Yes, I was trying to use Ampere's law. But why it is not applicable here? I though electron is moving in a circular path, so it supposes to be symmetrical? And when you said "You now have a current loop of known parameters (i and r) centered on the nucleus", how do I know the current?
     
  5. Oct 30, 2015 #4

    rude man

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    While Ampere's law is valid for any closed path pierced by the loop, the B field around it is not at all constant, so you cannot say that ∫B dl = B 2πr even though ∫B dl = μi is correct. So you can't evaluate B at any point around your path. Also, why did you include N in the Ampere formula?

    Figure out what the speed of the orbiting electron is around the loop. Then i = dq/dt at any point on the electron's orbit.
     
  6. Oct 30, 2015 #5
    can someone show work for this problem please
     
  7. Oct 30, 2015 #6
    can u please show work ?
     
  8. Oct 30, 2015 #7

    rude man

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    No, as The Prisoner (old TV show) was told, "That would be telling".
     
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