Examination of electromagnetic powers with the example of a Faraday disc dynamo

Abstract

This paper studies the mathematical form of electromagnetic powers and their influence on the balance of energy by using the example of a Faraday disc. First, two forms of energy (and balances thereof) are discussed. These employ different forms of powers, which can be distinguished w.r.t. their physical origins and their interpretations in context with the notions of supply and production. The stationary Faraday disc experiment is modeled following the description by Kovetz (Electromagnetic theory, Oxford University Press, Oxford, 2000). Concepts for formulating the electromagnetic field equations for the rotating disc are discussed, and the corresponding approximate analytical solutions are presented. Based on the obtained electromagnetic fields, the powers of the disc are analyzed for a stationary process. The conversion of mechanical power to heating and electromagnetic powering of an external resistor is explained. The paper concludes with the computation of the time evolution of the angular velocity for a magnetically induced breaking process of the disc.