Chapter 30, Problem 17P

You are working for a company that manufactures motors and generators. At the end of your first day of work, your supervisor explains to you that you will be assigned to a team that is designing a new homopolar generator. You have no idea what that is, but agree wholeheartedly to the assignment. At home that evening, you go online to learn about the homopolar generator and find the following. The homopolar generator, also called the Faraday disk, is a low-voltage, high-current electric generator. It consists of a rotating conducting disk with one stationary brush (a sliding electrical contact) at its axle and another at a point on its circumference as shown in Figure P30.17. A uniform magnetic field is applied perpendicular to the plane of the disk. When superconducting coils are used to produce a large magnetic field, a homopolar generator can have a power output of several megawatts. Such a generator is useful, for example, in purifying metals by electrolysis. If a voltage is applied to the output terminals of the generator, it runs in reverse as a homopolar motor capable of providing great torque, useful in ship propulsion. At work the next morning, your supervisor tells you that the homopolar generator under consideration will have a magnetic field of magnitude B = 0.900 T and the radius of the disk is r = 0.400 m. The desired emf to be generated with the device is $\mathcal{E}=25.0\text{V}$. Your supervisor asks you to determine the required angular speed of the disk to achieve this result.

Figure P30.17