30.5:
Faraday Disk Dynamo
The Faraday disk dynamo is a direct current generator that works on the principle of induction.
It consists of a conducting disk rotating with a constant angular velocity via a conducting shaft, which is placed in a uniform magnetic field perpendicular to the plane of the disk. The rotation of the disk induces a motional emf in it.
Consider a small segment of the disk with a velocity vector tangential to it. The magnetic force on this segment is radially outward. This accumulates free positive charges toward the rim and free negative charges toward the center, resulting in emf.
Integrating the equation of emf within the limits of the segment length and substituting the magnitude of the velocity vector gives the magnitude of the motional emf.
This disk can be connected to the circuit via two stationary brushes, which conduct the current across the closed loop.
According to Lenz's law, the induced current opposes the constant angular velocity of the disk. So, work must be done to keep the disk rotating at constant angular velocity.
30.5:
Faraday Disk Dynamo
A Faraday disk dynamo is a DC generator, producing an emf that is constant in time. It consists of a conducting disk that rotates with a constant angular velocity in the magnetic field, perpendicular to the disk's plane. The rotation of the disk causes a change in magnetic flux, which induces an emf, causing opposite charges to develop on the rim and in the center of the disk. The polarity of the induced emf can be determined by the direction of the magnetic field and the direction of the rotation of the disk. If the rotating disk is connected to an external circuit using brushes, then an induced current flows.
According to Lenz's law, the induced emf always opposes the cause producing it. For the Faraday disk dynamo, the induced emf opposes the rotation of the disk. Therefore, external power must be supplied to keep the disk rotating at a constant angular velocity.
The induced emf in such a dynamo can range from a few millivolts to a few volts. The magnitude of the induced emf can be further enhanced by connecting multiple generators in the series or by increasing the magnetic field's strength, the disk's radius, and the disk's angular velocity.
Suggested Reading
- Young, H.D and Freedman, R.A. (2012). University Physics with Modern Physics. San Francisco, CA: Pearson. Section 29.4, pages 971.