Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/291

 CHAPTER XII. CURRENT-SHEETS.

647.] A is an infinitely thin stratum of conducting matter, bounded on both sides by insulating media, so that electric currents may flow in the sheet, but cannot escape from it except at certain points called Electrodes, where currents are made to enter or to leave the sheet.

In order to conduct a finite electric current, a real sheet must have a finite thickness, and ought therefore to be considered a conductor of three dimensions. In many cases, however, it is practically convenient to deduce the electric properties of a real conducting sheet, or of a thin layer of coiled wire, from those of a current-sheet as defined above.

We may therefore regard a surface of any form as a current-sheet. Having selected one side of this surface as the positive side, we shall always suppose any lines drawn on the surface to be looked at from the positive side of the surface. In the case of a closed surface we shall consider the outside as positive. See Art. 294, where, however, the direction of the current is defined as seen from the negative side of the sheet.

648.] Let a fixed point $$A$$ on the surface be chosen as origin, and let a line be drawn on the surface from $$A$$ to another point $$P$$. Let the quantity of electricity which in unit of time crosses this line from left to right be $$\phi$$, then $$\phi$$ is called the Current-function at the point $$P$$.

The current-function depends only on the position of the point $$P$$, and is the same for any two forms of the line $$AP$$, provided this