Vector potentials electric dipole equivalence

VII. Lorenz Vector Potential without Scalar Potential Equivalent Electric Dipole... 

VII. LORENZ VECTOR POTENTIAL WITHOUT SCALAR POTENTIAL EQUIVALENT ELECTRIC DIPOLE... 

Then we have the same electric impulse in both cases. This gives the same electric gauge vector potential, 4,2. However, the Lorenz gauge potentials are quite different. For the electric dipole in Section VI, both 42 and 2 are zero. For the toroidal antenna equivalent electric dipole in Section VII, while 2 is zero, 42 is non zero. How then are these two cases different Within the gauge condition... 

In this appendix a general proof is given of the equivalence of the local field amplification matrix to the transpose of the dipole amplification matrix. Consider a piece of dielectric material of arbitrary shape placed in a uniform external electric field g. Let O be the origin of a coordinate system and fi denote the displacement vector to an arbitrary point in space. The electric field at py Er potential field in all of space... 

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