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 ωf. 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 (W=∫Ndϕ).
(b) Use Eq. 7.35 to determine the energy stored in the resulting magnetic field.