Tubes of force and bisurfaces in electromagnetism

Mathematics. Physics. Mechanics


Khrapko R. I.



Faraday's lines of force are not enough to an adequate graphical representation of electromagnetic fields. It is necessary to use surfaces. The surfaces permit to represent evidently, for example, a generation of a magnetic field by an electric current, or to represent a generation of scalar potential by an electric field. However, strictly speaking, it is necessary to use tubes instead of lines, and bisurfaces instead of surfaces. A conception of differential (exterior) forms and pseudo forms is used for an explanation. We speak that an external differentiation of a form results in its boundary and the integration of a form by the Biot-Savarat formula results in a new form named as termination. The termination of a termination is zero, the same as the boundary of a boundary. A boundary is closed. A termination is sterile. A conjunction is considered. The conjunction converts forms to pseudo forms and back, converts closed forms to sterile forms and back. The conjunction permits to construct chains of the forms.The conjunction differs from the Hodge star operation by an absence of the dualization.

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