Maxwell's Equations and Lorentz Transformation

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SUMMARY

This discussion focuses on proving the invariance of Maxwell's equations under Lorentz Transformation, specifically addressing the equation "∇·B = 0". The user, a third-year student, expresses difficulty in demonstrating this invariance due to a term that fails to cancel out. The conversation emphasizes the need for a clear example to aid understanding, particularly for those not yet familiar with tensor calculus.

PREREQUISITES
  • Understanding of Maxwell's equations
  • Basic knowledge of vector calculus, including gradient, divergence, and curl
  • Familiarity with Lorentz Transformation principles
  • Introductory physics concepts related to electromagnetism
NEXT STEPS
  • Study the mathematical foundations of tensor calculus
  • Learn about the derivation of Maxwell's equations in different reference frames
  • Explore the implications of Lorentz invariance in electromagnetism
  • Review examples of applying divergence and curl in vector fields
USEFUL FOR

Students studying electromagnetism, physics enthusiasts, and educators seeking to clarify the relationship between Maxwell's equations and Lorentz Transformation.

jomel_maroma
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Hi! I'm having problems with this homework my professor gave us this morning: Prove that Maxwell's equations is invariant under Lorentz Transformation.

I'm just currently in third year, and we haven't been taught tensors yet. The extent of what I know mathematically is only until gradient, divergence, curl, and the like.

I've been trying to do the "∇.B=0" one but there always is a term that doesn't cancel out. Can anyone show me how to do it? ^I just need an example. Thank you!
 
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