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The Continuity Equation for a time varying field Eris:
dEr/cdt = Del.Ev where Ev is the vector field associated with the real time varying field.
Er + Ev =E, constitute a quaternion field.
Del.Ev is the Divergence of the vector field.
The Continuity Equation is a statement that the time variation of the real field is equal to the Divergence of the vector field. or more succinctly, the quaternion field E=Er + Ev is Real invariant.
The Vector part of the variation is 0= dEv/cdt + Del Er + DelxEv , this is Vector Invariance of E. This is not the Continuioty Equatin but the Induction Equation. Together they represent the Invariance of the quaternion field E=Er + Ev.
Because quaternions are not taught in schools yet, few realize the relationship between Continuity and Induction, they are the Real and Vector parts of Invariance!
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What has the author John L Lewis written?
John L. Lewis has written: 'The method of layer potentials for the heat equation in time-varying domains' -- subject(s): Heat equation, Singular integrals 'Marriage' 'Science in Society'
