Slovník pojmůHertz vectorAssume ideal dielectrics, which is polarized by the external electric field. The vector of enforced electric polarization Pvn describes polarization. Then, electric displacement vector can be expressed as Substituting electric displacement vector D (1) to the first Maxwell equation, and assuming zero enforced current Jvn = 0 (induced current is zero too, because the ideal dielectrics is of zero conductivity)
Then, the third Maxwell equation can be rewritten to
On the basis of (2) and (3), wave equation for vector potential can be obtained
For the scalar potential, we get
We express potentials A and φ using an auxiliary vector Πe
Substituting (6) to wave equation (4) and (7) to (5), we get
| . | ( 8 ) |
| . | ( 9 ) |
If vector πe is determined to meet the equation
even (8) and (9) are met at the same time. That way, solution of Maxwell equations is transformed to the solution of a single inhomogeneous equation when Jvn = 0. Hertz discovered this possibility, and the vector Πe is therefore called electric Hertz vector. In dual way, magnetic Hertz vector can be introduced. Zpět
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