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!

Spinning iron wire

  1. Aug 20, 2013 #1
    1. The problem statement, all variables and given/known data

    Iron atoms (atomic mass 56) contain two free electron spins that can align with an external magnetic field. An iron wire 3 cm long and 1 mm in diameter is suspended vertically and is free to rotate about its axis. A strong magnetic field parallel to the wire's axis is applied. How large is the resulting change in its angular velocity.

    2. Relevant equations

    [tex] \oint \vec{E} \cdot \vec{dl} = - \frac{d}{dt} \int \vec{B} \cdot \vec{da} [/tex]

    Poynting vector: [itex] \vec{S} = \mu_0 \vec{E} \times \vec{B} [/itex].

    Bohr's magneton might come in handy: [itex] \mu_b = \frac{e \hbar}{2 m_e} [/itex]

    3. The attempt at a solution

    My first thought was to find the Poynting vector because the angular momentum contained in the fields is proportional to [itex] \vec{r} \times \vec{S} [/itex]. Assuming the wire is in the z direction, we can write that the applied magnetic field is [itex] \vec{B} = B \hat{z} [/itex]. This would create a magnetic flux through the x-y plane, and hence create an electric field in the [itex] \hat{\phi} [/itex] direction from the Faraday law. But that means that [itex] \vec{S} \approx \hat{\phi} \times \hat{z} = \hat{r} [/itex] and therefore there would be no angular momentum change in the fields.

    I feel this is too simplistic and possibly wrong, especially since we didn't use any of iron's properties.
     
  2. jcsd
  3. Aug 20, 2013 #2
    So as always I overcomplicate stuff. It is easy to just calculate L = N hbar/2, where N is the number of spin, given the density of iron. L = I w, where I is the moment of inertia. Super simple. Ugh.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Spinning iron wire
  1. Iron bar bending force (Replies: 1)

Loading...