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: Imperfectly conducting sphere spinning in a homogeneous B-field

  1. Oct 5, 2007 #1
    1. The problem statement, all variables and given/known data
    Link to assignment
    The fact that it is imperfectly conducting is supplied so that the charges in the sphere will move with the same angular velocity.
    The B-field induced by the moving charges will be disregarded.

    2. Relevant equations
    [tex]\vec{F}[/tex]=0 => [tex]\vec{E}[/tex]=-[tex]\vec{v}[/tex][tex]\times[/tex][tex]\vec{B}[/tex]
    The equations above apply inside the sphere. And lead to the E-field inside.

    3. The attempt at a solution
    I have found the E-field inside, and the volume charge density inside.

    This gives the potential inside (have set the potential at r=0 to V_0)
    V(r)= V_0 - [tex]\frac{1}{2}[/tex]B[tex]\omega[/tex]r^2 (sin [tex]\theta[/tex])^2

    The total charge inside and the total charge on the surface are excactly equal but opposite as one would expect. total charge = 0
    Q_inside = -[tex]\frac{8}{3}[/tex][tex]\pi[/tex][tex]\epsilon_{0}[/tex]B[tex]\omega[/tex]R^3

    Q_surface = [tex]\frac{8}{3}[/tex][tex]\pi[/tex][tex]\epsilon_{0}[/tex]B[tex]\omega[/tex]R^3

    Then the problem is to find the potential and E_field outside the sphere. I can't seem to figure out if the charges on the surface are the only ones contributing.
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
    Last edited: Oct 5, 2007
  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