Equivalence of Derivations in the Wave Equation from Maxwell's Equations

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SUMMARY

The discussion centers on the derivation of the wave equation from Maxwell's equations, specifically addressing the equivalence of two derived equations: equation (4) from the textbook and equation (5) produced by the user. The user identifies a discrepancy in a single term between the two equations and seeks clarification on their equivalence. The conclusion reached is that equations (4) and (5) are indeed equivalent, and the transition from (5) to (4) can be achieved using the chain rule.

PREREQUISITES
  • Understanding of Maxwell's Equations
  • Familiarity with wave equations in physics
  • Knowledge of calculus, specifically the chain rule
  • Ability to manipulate algebraic equations
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  • Study the derivation of the wave equation from Maxwell's Equations in detail
  • Review the application of the chain rule in calculus
  • Explore the implications of different terms in wave equations
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Students of physics, particularly those focusing on electromagnetism and wave phenomena, as well as educators seeking to clarify the derivation process of wave equations from Maxwell's equations.

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Homework Statement


I am actually following the derivation of the wave equation from Maxwell equations. And I do not understand one step, because in the task for the derivation I get a slightly different result (maybe they are equivalent, but I am not sure).

Homework Equations


In the attached file:
(1) - starting equation; (2) and (3) - necessary identities; (4) - final result from the book; (5) - my final result.

The Attempt at a Solution


(5) is the equation I got. As you can see, only one term is different. Is equation (5) equivalent then to equation (4)? If yes, how to get from (5) to (4)? If no, what could be incorrect?
 

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(4) and (5) are equivalent. Use the chain rule.
 

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