Torque on a rotating solid conducting cylinder in B field

1. Nov 26, 2012

merrypark3

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 $\stackrel{\rightarrow}{ω}$

j=σ(u×B)=ρv=σ((ω×r)×B)
$\stackrel{\rightarrow}{j}=σ((\stackrel{\rightarrow}{ω}×\stackrel{\rightarrow}{r}) ×\stackrel{\rightarrow}{B})=ρ\stackrel{\rightarrow}{v}$

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

Is it right?

2. Nov 27, 2012

TSny

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