Lorenz guage and equation of continuity

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SUMMARY

The discussion centers on demonstrating that the Lorentz gauge equation, represented as ∇·A = -µ(jωε+σe)φ, is equivalent to the equation of continuity, ∇·Ji = (jωε+σe)/ε P(R). Participants suggest starting by taking the gradient of both sides of the Lorentz gauge equation and then applying the curl to the resulting equation. The substitution of the expression ∇φ = -E - ∂A/∂t is also recommended as a crucial step in the derivation process.

PREREQUISITES
  • Understanding of vector calculus, specifically divergence and curl operations.
  • Familiarity with electromagnetic theory, particularly Ampère's law and Faraday's law.
  • Knowledge of the Lorentz gauge condition in electrodynamics.
  • Basic proficiency in differential equations and their applications in physics.
NEXT STEPS
  • Study the derivation of the Lorentz gauge condition in electrodynamics.
  • Learn about the continuity equation in electromagnetism and its implications.
  • Explore vector calculus techniques, focusing on divergence and curl.
  • Investigate the relationship between electric fields and potentials in electromagnetic theory.
USEFUL FOR

Students and professionals in physics, particularly those specializing in electromagnetism, as well as educators seeking to clarify the relationship between the Lorentz gauge and the equation of continuity.

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

Homework Statement


Show that Lorentz' gauge 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?
 
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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 \mathbf{\nabla}\varphi=-\textbf{E}-\frac{\partial \textbf{A}}{\partial t}[/tex]
 
Starting from continuity Equation, how to reach Lorenz guage?

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


gabbagabbahey said:
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 \mathbf{\nabla}\varphi=-\textbf{E}-\frac{\partial \textbf{A}}{\partial t}[/tex]
 

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