# Homework Help: 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