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Lorenz guage and equation of continuity

  • #1
634
1
π²³ ∞ ° → ~ µ ρ σ τ ω ∑ … √ ∫ ≤ ≥ ± ∃ · θ φ ψ Ω α β γ δ ∂ ∆ ∇ ε λ Λ Γ ô

Homework Statement


Show that Lorentz' guage equation
∇.A = -µ(jωε+σe

is the equation of continuity

∇ .Ji = (jωε+σe)/ε P(R)

Homework Equations





The Attempt at a Solution



I tried taking curl, div of ampere's law, faraday's law but got nowhere.
Any clue or hint?

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
gabbagabbahey
Homework Helper
Gold Member
5,002
6
You might start by taking the gradient of each side of the Lorentz Gauge equation, and then maybe taking the curl of each side of the resulting equation after substituting [itex]\mathbf{\nabla}\varphi=-\textbf{E}-\frac{\partial \textbf{A}}{\partial t}[/tex]
 
  • #3
1
0
Starting from continuity Equation, how to reach Lorenz guage?

I have tried everything, but I failed. Any hint would be appreciated.


You might start by taking the gradient of each side of the Lorentz Gauge equation, and then maybe taking the curl of each side of the resulting equation after substituting [itex]\mathbf{\nabla}\varphi=-\textbf{E}-\frac{\partial \textbf{A}}{\partial t}[/tex]
 

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