Page:Elementary Text-book of Physics (Anthony, 1897).djvu/335

§ 278] of the original circuit. If then, in a circuit containing no impressed electromotive force, or in which $$E = 0,$$ there be brought an arrangement of uncombined chemical substances which are capable of combination, or if in its presence a magnet be moved, or if a junction of two dissimilar parts of the circuit be heated, there will be set up an electromotive force $$\frac{A}{t},$$ and a current $$I = \frac{A}{tR}\cdot$$ Any of these methods may then be used as the means of generating a current. The first gives the ordinary battery currents of Volta, the second the induced currents discovered by Faraday, and the third the thermoelectric currents of Seebeck.

This demonstration fails when applied to the case of the induction of one current by another, in consequence of the changes produced in both by their mutual interactions. The correct demonstration in this case can only be reached by the aid of the dynamical equations of the electromagnetic field.

278. Poynting's Theorem.—On the view that the current consists of the disappearance of tubes of force in the conductor, the energy developed in the circuit enters it from the dielectric. By choosing a very simple case we may determine the rate at which this energy moves through the dielectric and into the conductor. We will suppose the current maintained in a very long straight cylindrical wire stretched between two parallel and very large planes, which are kept at the potentials $$V_{1}$$ and $$V_{2}.$$ In such an arrangement the tubes of force are cylindrical, passing perpendicularly between the two plates and parallel with the conductor joining them; the electrical force in such a field is everywhere the same. Now consider a plane parallel with the plates, and describe in it a circle having any radius $$r$$ with its centre at the centre of the wire. Let $$N$$ represent the number of tubes of force which pass through unit area in this plane, and $$v$$ the velocity with which these tubes of force pass through the circumference of the circle of radius $$r.$$ Then the number of tubes which pass through this circumference in unit time is $$2\pi rv N,$$ and since the current is supposed to