Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/102

62 the displacement, $$ \delta E$$ = $$ \delta e$$, and since $$E$$ and $$e$$ vanish together, $$E=e$$, or—

The displacement outwards through any spherical surface concentric with the sphere is equal to the charge on the sphere.

To fix our ideas of electric displacement, let us consider an accumulator formed of two conducting plates $$A$$ and $$B$$, separated by a stratum of a dielectric $$C$$. Let $$W$$ be a conducting wire joining $$A$$ and $$B$$, and let us suppose that by the action of an electromotive force a quantity $$Q$$ of positive electricity is transferred along the wire from $$B$$ to $$A$$. The positive electrification of $$A$$ and the negative electrification of will produce a certain electromotive force acting from $$A$$ towards in the dielectric stratum, and this will produce an electric displacement from $$A$$ towards $$B$$ within the dielectric. The amount of this displacement, as measured by the quantity of electricity forced across an imaginary section of the dielectric dividing it into two strata, will be, according to our theory, exactly $$Q$$. See Arts. 75, 76, 111.

It appears, therefore, that at the same time that a quantity $$Q$$ of electricity is being transferred along the wire by the electromotive force from $$B$$ towards $$A$$, so as to cross every section of the wire, the same quantity of electricity crosses every section of the dielectric from $$A$$ towards $$B$$ by reason of the electric displacement.

The reverse motions of electricity will take place during the discharge of the accumulator. In the wire the discharge will be $$Q$$ from $$A$$ to $$B$$, and in the dielectric the displacement will subside, and a quantity of electricity $$Q$$ will cross every section from $$B$$ towards $$A$$.

Every case of electrification or discharge may therefore be considered as a motion in a closed circuit, such that at every section of the circuit the same quantity of electricity crosses in the same time, and this is the case, not only in the voltaic circuit where it has always been recognised, but in those cases in which electricity has been generally supposed to be accumulated in certain places.

61.] We are thus led to a very remarkable consequence of the theory which we are examining, namely, that the motions of electricity are like those of an incompressible fluid, so that the total quantity within an imaginary fixed closed surface remains always the same. This result appears at first sight in direct contradiction to the fact that we can charge a conductor and then introduce