Induced Electric Fields in Coaxial Geometry

Although electromagnetic theory has been known for a century, and Biot's (also called Ampere's) formula in its simple form, dH = (1/4π)(Idl sinθ/r2), is often used, the corresponding relationship, dE = −(1/4π) (φdl sinθ/r2), for the electric field induced in space by a filament of time-varying magnetic flux, seems not to have been recognized or used to any great extent. The discussion here presented, using the example afforded by coaxial conductors, illustrates some aspects of how this latter relationship may be used to solve for induced electric fields, including those for coaxial systems of both finite and infinite length with hollow or solid center conductors. The magnetically induced electric field fringes outward near the shorted end of a coaxial system, and a method is shown for finding the radial positions of a given line of electric force when coaxial conductors of different dimensions are connected together.