Voltage and electromotive force or emf are very fundamental quantities in engineering, physics and technology. Yet there are few texts on these quantities that are suitable for advanced under graduates or graduate students at university. A rigorous derivation of a formula for the calculation of emf that is based on the velocity of the conductors through magnetic fields is presented. Attention is devoted to emf calculation in rigid and nonrigid configurations. Numerous examples of its use are given and worked from the viewpoint of various observers. Complete field solutions are given to verify assumptions commonly made in calculating emf. Many long standing apparent paradoxes and general fallacies concerning Faraday disc generators are explained several different ways. A complete three dimensional solution is given for the Faraday like disc generator of Foucault. and Le Roux. It is shown how the calculation of emf is expedited by the special theory of relativity set forth by Albert Einstein in 1905. The Maxwell-Lorentz Transformation is used to extend the calculation of emf to include dielectrics and electrically conducting fluids in motion. The constitutive equations of media are studied in cases involving relative motion. Cases are disclosed where the fields may be zero to one observer and not zero to another.
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