Electromagnetism Homogeneous Wave Equation

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SUMMARY

The discussion focuses on deriving the homogeneous electromagnetic wave equation from Maxwell's equations, specifically concerning the magnetic field (H). The equation is expressed as ∇²H - (∂²B/∂t²) * (1/c²) = 0. Participants seek strategies for solving this equation for H(z,t) by utilizing the relationship between the magnetic field B and H, emphasizing the importance of media type in simplifying the equation further.

PREREQUISITES
  • Understanding of Maxwell's equations
  • Familiarity with electromagnetic wave propagation
  • Knowledge of vector calculus, particularly the Laplacian operator
  • Concept of wave equations in different media
NEXT STEPS
  • Study the derivation of the electromagnetic wave equation from Maxwell's equations
  • Learn about the relationship between magnetic field (H) and electric field (E) in electromagnetic waves
  • Explore methods for solving partial differential equations, specifically in the context of wave equations
  • Investigate the effects of different media on electromagnetic wave propagation
USEFUL FOR

Physicists, electrical engineers, and students studying electromagnetism who are looking to deepen their understanding of wave equations and their applications in various media.

donmacaroni
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I've managed to derive from Maxwell's equations the homogeneous electromagnetic wave equation with respect to the magnetic field.

(The one that goes Del Squared of H minus (The second order partial derivative of B multiplied by the recipricol of C squared all equal to zero) Hopefully that makes sense)

Can anyone help me in giving me a strategy for solving this equation for H(z,t)?
 
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Use the relationship between B & H to reduce it to all H. To simplify further you will need to refer to the problem specification with regards to the type of media you are dealing with. Hopefully by that point you can see what to do.
 

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