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Torque on a rotating solid conducting cylinder in B field

  1. Nov 26, 2012 #1
    1. The problem statement, all variables and given/known data
    panofsky 10.3

    Find the torque on a solid conducting cylinder rotating slowly in a uniform magnetic field perpendicular to the axis of the cylinder.





    3. The attempt at a solution

    let the radius of cylinder r, and the conductivity is σ, the rotating angular velocity is [itex]\stackrel{\rightarrow}{ω}[/itex]

    j=σ(u×B)=ρv=σ((ω×r)×B)
    [itex]\stackrel{\rightarrow}{j}=σ((\stackrel{\rightarrow}{ω}×\stackrel{\rightarrow}{r}) ×\stackrel{\rightarrow}{B})=ρ\stackrel{\rightarrow}{v}[/itex]


    [itex]\stackrel{\rightarrow}{τ}=∫(ρ\stackrel{\rightarrow}{v}×\stackrel{\rightarrow}{B} )dV=0[/itex]
    1. The problem statement, all variables and given/known data

    Is it right?
     
  2. jcsd
  3. Nov 27, 2012 #2

    TSny

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    Homework Helper
    Gold Member

    The net torque will not be zero. Your last integral looks like the net force rather than the net torque. Otherwise your expressions look ok to me if ##\vec{v}## denotes the drift velocity of charge carriers. I don't think using ##\rho \vec{v}## for ##\vec{j}##will help much.
     
    Last edited: Nov 27, 2012
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