Electrical Papers volume 2

Cover Electrical Papers volume 2
Electrical Papers volume 2
Oliver Heaviside
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(31) indicating that the sum of the activities of the impressed forces, or the energy added to the system per second, equals the total dissipativity Q, plus the rate of increase of the stored energies, electric and magnetic, throughout the system. Now here F is circuital; if, therefore, the distribution of e be polar, or e be the vector space-variation of a single- valued scalar potential, of which a simple closed shell of impressed force is an example, the left member of (31) vanishes, so that... the dis- sipation, if any, is derived entirely from the stored energy. Start, then, with no electric or magnetic energy in the system ; then the positivity of Q, U, and T ensures that there never can be any, under the influence of polar impressed force. Hence two shells of impressed force of equal uniform strength produce the same fluxes if their edges be the same ; not merely the steady fluxes possible, but the variable fluxes anywhere at corresponding moments after commencing action. The only difference made when one shell is substituted for the other is in the manner of the transfer of energy at the places of impressed force; for we have to remember that the effective force producing a flux, or the "force of the flux, " equals the sum of the impressed force and the " force of the field " ; whereas the transfer of energy is determined by the vector product of the two forces of the field, electric and magnetic respectively.

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