On the applicability limits of some ‘infinite’ models in the course of electricity and magnetism

We present a quantitative analysis of some ‘infinite’ models, occurring in the course of electricity and magnetism. First, we estimate the deviations from the models of an ideal parallel-plate capacitor and solenoid arising due to the bending field effect. Next, we consider the models of an infinite wire and plane of uniform charge. We show that in the first case the real electric field differs from the idealized one because of the finite length of the wire. In the second case this difference is caused also by the non-uniform surface charge density. The issues outlined in this article will be useful for advanced undergraduates, studying solutions to electrostatic and magnetostatic problems.

Keywords
limit transition models; parallel-plate capacitor; solenoid; infinite charged wire; infinite charged plane