1. Not finding help here? Sign up for a free 30min 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!

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]=Q[[tex]\vec{E}[/tex]+[tex]\vec{v}[/tex][tex]\times[/tex][tex]\vec{B}[/tex]]
    [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.
    E=B[tex]\omega[/tex]x[tex]\hat{x}[/tex]+B[tex]\omega[/tex]y[tex]\hat{y}[/tex]
    [tex]\rho[/tex]=-2B[tex]\omega[/tex][tex]\epsilon_{o}[/tex]

    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?



Similar Discussions: Imperfectly conducting sphere spinning in a homogeneous B-field
Loading...