Geodesics and Motion in an EM Field

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SUMMARY

The discussion centers on the calculation of geodesics in an electromagnetic (EM) field, specifically addressing the differentiation of the term q A_b with respect to the parameter lambda. The participant identified a mistake in their initial approach, realizing that the chain rule introduces an additional term that is crucial for accurate computation. This insight leads to a more complete understanding of the motion of charged particles in an EM field.

PREREQUISITES
  • Understanding of differential geometry and geodesics
  • Familiarity with electromagnetic field theory
  • Knowledge of the chain rule in calculus
  • Experience with mathematical notation and partial derivatives
NEXT STEPS
  • Study the application of the chain rule in vector calculus
  • Explore the mathematical formulation of geodesics in curved spacetime
  • Research the role of electromagnetic potentials in particle dynamics
  • Investigate advanced topics in differential geometry related to EM fields
USEFUL FOR

Physicists, mathematicians, and students studying theoretical physics, particularly those focusing on electromagnetism and general relativity.

Woolyabyss
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Homework Statement
I've attached the problem statement as an image.
Relevant Equations
Euler Lagrange equations
I've also attached my attempt as a pdf file. My main issue seems to be I only get one A partial term. Any help would be appreciated.
 

Attachments

  • electro.png
    electro.png
    29.4 KB · Views: 428
  • electro solution.pdf
    electro solution.pdf
    46.3 KB · Views: 383
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I've just realized my mistake. the partial of q A_b with respect to lambda isn't zero, you get an extra term from the chain rule and it works out nicely.
 

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