An infinite cylinder of radius R carries a uniform surface charge density o. We propose to...

  

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An infinite cylinder of radius R carries a uniform surface charge density o. We propose to set it spinning about its axis, at a final angular velocity ws. 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, inside and outside the cylinder, in terms of w, dw/dt and s (the distance from the axis). Calculate the torque you must exert, and from that obtain the work done per unit length. If needed, you can apply Biot-Savart law for time varying currents. (b) Use W = JAll universe magnetic field. B²dr to determine the energy stored in the resulting %3D An infinite cylinder of radius R carries a uniform surface charge density o. We propose to set it spinning about its axis, at a final angular velocity ws. 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, inside and outside the cylinder, in terms of w, dw/dt and s (the distance from the axis). Calculate the torque you must exert, and from that obtain the work done per unit length. If needed, you can apply Biot-Savart law for time varying currents. (b) Use W = JAll universe magnetic field. B²dr to determine the energy stored in the resulting %3D