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The derivations below are for the Acceleration Potentials external to the source. Derivations for the Potentials internal to the source follow the same process with the same results. B.1 Curl of the Spatial Acceleration Potential Vector. The spatial Acceleration Potential vector, As, has only one component, in the s direction, and therefore by the definition of curl, the 4-vector curl of As, is zero, i.e.
B.2 Curl of the Temporal Acceleration Potential Vector. The temporal Acceleration Potential vector At, has only one component, in the x0 direction and therefore by the definition of curl, its 4-vector curl is zero. However, because At, is a function of s, it is necessary to prove this.
By (B.1) this reduces to
Because u is only a function of s, the gradient in (B.3) can be
written
Substituting for u and carrying out the partial differentiation gives
and therefore
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P.G.Bass, Agust 2009
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