Question

You are working for a company that produces generators for windmills. To test various designs, you have been tasked with building a laboratory that measures the voltage output from a generator. Before spending a lot of time, effort, and money you decide to set up a simple model of a generator for which you can calculate what to expect. Your model consists of Helmholtz coils to generate a well-defined magnetic field and a smaller coil of wire, in between the Helmholtz coils, to generate the voltage difference. The small coil is mounted to a motor so that it spins at a uniform speed. You will need to determine how the expected voltage difference may depend on time, the rate of small coil rotation, and other parameters in your setup.

1. For the magnetic field at some random angle to the plane of the small coil, draw a picture showing only the small coil, a vector giving the direction of the magnetic field, the area vector for the coil, and the angle between the magnetic field and the area vector. 2. Write an equation for the magnetic flux through the small coil at an instant of time when the area vector is at some angle to the magnetic field. 3. Write an expression that shows how the magnetic flux through the small coil changes as it turns with a constant angular speed. 4.Calculate the voltage difference produced by a coil of wire spinning in a uniform magnetic field as a function of its angular speed.

Answer 1