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Homework Help: 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]

    [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


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    Homework Helper
    Gold Member
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    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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