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A homopolar generator (also called a Faraday disk generator in honor of Faraday, who built the first one) is portrayed above: a conducting disk with radius a is forced to rotate at a constant angular speed ω in a uniform magnetic field of magnitude B perpendicular to and into the page. A wire is connected to its (conducting) axle, and a second wire brush is in continuous contact with the rim. A resistive load R completes the circuit. a) What direction do you expect current to flow through the resistor R (draw arrow onto figure)? b) Note that the speed of a conduction charge in the magnetic field will depend on the radius of the charge from the center of the disk. Integrate the magnetic force on the charge from the center to the rim and use the result to compute the voltage produced by the generator. Express the result in terms of the period of rotation; T = 2π/ω. Compare the result to the magnetic flux swept out by the disk per unit time. Compute the flux as the entire area of the disk times the magnetic field strength. Is it the same? Different? Find the current I through R.
Submitted by Angela D. Sep. 07, 2021 07:21 p.m.
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