1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Magnetic Field Seen by Orbiting Electron

  1. Apr 26, 2012 #1
    1. The problem statement, all variables and given/known data

    What is the magnetic field seen by an electron in the first Bohr orbit of hydrogen due to the intrinsic spin moment of the proton?

    2. The attempt at a solution

    I think I've got it; but might be way off.

    A charged nucleus with velocity -v constitutes a current element j,
    [tex]\mathbf j = -Ze \mathbf v [/tex]
    Ampere's law then gives
    [tex]\mathbf B = - \frac{Ze\mu}{4\pi} \frac{\mathbf v \times \mathbf r}{r^{3}}[/tex]
    Coulomb's law
    [tex]\mathbf E = - \frac{Ze}{4\pi \epsilon}\frac{\mathbf r}{r^{3}}[/tex]
    and thus
    [tex]\mathbf B = - \frac{1}{c^{2}}\mathbf v \times \mathbf E[/tex]
    The spin-orbit interaction energy is found to be
    [tex]\Delta E = \frac{1}{2} \frac{g \mu}{\hbar} \mathbf S \cdot \mathbf B[/tex]
    Applying the electric field E and the force F acting on the electron
    [tex]-e \mathbf E = \mathbf F[/tex]
    [tex]\mathbf F = - \frac{dV(r)}{dr}\frac{\mathbf r}{r}[/tex]
    and so finally
    [tex]\mathbf B = - \frac{1}{ec^{2}}\frac{1}{r}\frac{dV(r)}{dr}\mathbf v \times \mathbf r[/tex]
    [tex]\mathbf B = - \frac{1}{emc^{2}}\frac{1}{r}\frac{dV(r)}{dr}\mathbf{L} [/tex]
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted