By Yuejin Z., Guodong X.
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Additional info for 3D magnetic field computation of a permanent magnet disc-type generator using scalar potential method
At 40 amperes, these electrons move at a velocity v ≈ 4 m/sec. The total length l of wire is about 103 meters, so the total electronic charge in the magnet is about 104 coulombs. 24) Carver A. Mead Aug. 8 Multiturn Coils 25 For comparison, the mass of a free electron is approximately 10−30 kg, and the rest mass of a proton is a factor of 1800 larger than that of an electron. The electromagnetic mass of an electron in our magnet is thus a factor of 109 larger than the rest mass of a free electron.
Because Eq. 12 is linear in the current, we can build up a solution by taking each current element, multiplying by its inverse distance from the point of measurement, and adding up such elementary vector contributions from all of space, which is exactly the meaning of the integral. So the form of the solution to the diﬀerential equation is the same as the form of the Green’s function. What about the magnitude? Eq. 13 tells us that the second derivative of the vector potential is proportional to the current density.
We shall return to this sign convention when we consider the propagation of a step function. 3 The Riemann–Sommerfeld Equation Maxwell (p. 490 in Ref. 33) quotes an important precursor to the four-vector expression of electrodynamics as follows: In a memoir presented to the Royal Society of G¨ ottingen in 1858, but afterwards withdrawn, and only published in 10 The Lorentz transformation (Eq. 7) of this vector reduces to Eq. 1 in the special case where x = x = 0 when t = t = 0. 11 Note that J does not contain displacement current.
3D magnetic field computation of a permanent magnet disc-type generator using scalar potential method by Yuejin Z., Guodong X.