By Carver A. Mead
ISBN-10: 0262632608
ISBN-13: 9780262632607
Carver Mead deals a significantly new method of the normal difficulties of electromagnetic concept.
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Additional resources for Collective Electrodynamics: Quantum Foundations of Electromagnetism
Sample text
There is an electric field E along the loop, the line integral of which is the voltage V between the ends. From a classical point of view, Newton’s law tells us that the force q0 E on a charge should be equal to the time rate of change of momentum. From Eq. 17) Carver A. Mead Aug. 6 Electrodynamic Momentum 21 Integrating the second form of Eq. 17 with respect to time, we recover Eq. 7, so the classical idea of inertia is indeed consistent with the quantum behavior of our collective system. Electrodynamic inertia acts exactly as a classical mechanical inertia: It relates the integral of a force to a momentum, which is manifest as a current.
Substituting A(r0 ) from these two expressions gives A0 = µ0 Jr02 /2 for the vector potential at the origin. 15) The latter procedure also serves to eliminate any residual concerns that we may have been harboring about the possible divergence of A at r = 0. Thus, we have two methods for evaluating the vector potential from an arbitrary distribution of current; in showing their equivalence in this simple case, we have seen how each approach complements the other. 6 Electrodynamic Momentum Feynman commented on the irrelevance of the concept of force in a quantum context.
17 with respect to time, we recover Eq. 7, so the classical idea of inertia is indeed consistent with the quantum behavior of our collective system. Electrodynamic inertia acts exactly as a classical mechanical inertia: It relates the integral of a force to a momentum, which is manifest as a current. We note that for any system of charges that is overall charge neutral, as is our superconductor, the net electromagnetic momentum is zero. For the −q A of each electron, we have a canceling +q A from one of the background positive charges.
Collective Electrodynamics: Quantum Foundations of Electromagnetism by Carver A. Mead
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