The first part of this article is a discussion of some ambiguities and sources of confusion in the presentation of electromagnetic induction in introductory texts. Particular attention is paid to the use of special relativity theory in these presentations. The second part of the paper discusses various examples of electromagnetic induction that have acquired reputations as “exceptions to the flux rule”. The origin of these exceptions is traced to an inappropriate choice of contour or its motions. We explicitly show that in these examples no exceptions occur, and give a general prescription for evaluating induced emf's.

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We review the Dirac formalism for dealing with constraints in a canonical Hamiltonian formulation, discuss gauge freedom, and display constraints for gauge theories in a general context. We introduce the Dirac bracket and show that it provides a consistent method to remove any gauge freedom present. We discuss stability in evolution of gauge theories and show that fixing all gauge freedom is sufficient to ensure well-posedness for a large class of gauge theories. Electrodynamics provides examples of the methods outlined for general gauge theories. Future work will apply the formalism, and results derived here, to General Relativity.