Abstract
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.
Highlights
Ones of the most important limit transition abstractions [1] in the university course of electricity and magnetism are the so-called ‘spatially infinite’ models. These include the models of physical objects, whose dimensions in one or several directions are so large that, when solving a specific problem, the influence of edge effects, that is, the presence of edges in these directions, can be neglected
One can distinguish between two types of models of this kind: 1. The models of objects ‘transverse’ and ‘longitudinal’ sizes of which differ many times
The models of objects, the distances to the edges of which from the observation points are much larger than the shortest distances from these points to the objects
Summary
Ones of the most important limit transition abstractions [1] in the university course of electricity and magnetism are the so-called ‘spatially infinite’ models. These include the models of physical objects, whose dimensions in one or several directions are so large that, when solving a specific problem, the influence of edge effects, that is, the presence of edges in these directions, can be neglected. One can distinguish between two types of models of this kind: 1. The first type includes, in particular, the models of an ideal parallel-plate capacitor and solenoid. We discuss the applicability limits of some other ‘infinite’ models in the course of electricity and magnetism. For education purposes the accuracy of a model, i.e. the errors arising as a consequence of neglecting several factors considered
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
