In this paper, we analyze a mixed form of a time-dependent eddy current problem formulated in terms of the electric fieldE<\/mml:mi>\\boldsymbol {E}<\/mml:annotation><\/mml:semantics><\/mml:math><\/inline-formula>. We show that this formulation admits a well-posed saddle point structure when the constraints satisfied by the primary unknown in the dielectric material are handled by means of a Lagrange multiplier. We use N\u00e9d\u00e9lec edge elements and standard nodal finite elements to define a semi-discrete Galerkin scheme. 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