An infinite cylinder of radius R carries a uniform surface charge σ. We propose to set i...

An infinite cylinder of radius R carries a uniform surface charge σ. We propose to set it spinning about its axis, at a final angular velocity ω_f . How much work will this take, per unit length? Do it two ways, and compare your answers:

(a) Find the magnetic field and the induced electric field (in the quasistatic approximation), inside and outside the cylinder, in terms of ω, ?ω, and s (the distance from the axis). Calculate the torque you must exert, and from that obtain the work done per unit length

(b) Use Eq. 7.35 to determine the energy stored in the resulting magnetic field.