Direct calculation of the electric field induced by a time-varying magnetic induction

This paper deals with the problem of obtaining the electric field near a region of magnetic flux, whose geometry has cylindrical symmetry. We derive an expression for a direct calculation of the induced electric field vector in geometric situations where a slowly varying magnetic field is confined to a long solenoid of arbitrary cross section. We check our result in a standard case, then we use it in a nontrivial case to confirm its utility. The developed expression can also be used to provide numerical evaluation of the field within the class of cylindrical symmetry. (C) 1996 American Association of Physics Teachers.