Transformation to a r. frame in which E and B are parallel

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SUMMARY

The discussion focuses on problem 11.15 from Jackson's "Classical Electrodynamics," which involves transforming to a reference frame where the electric field E and magnetic induction B are parallel. The electric field Eo is aligned with the x-axis, while the magnetic induction Bo, equal to 2Eo, lies in the xy-plane at an angle theta. The key solution involves applying a Lorentz transformation, specifically a boost in the z-direction, to achieve the desired alignment of the fields.

PREREQUISITES
  • Understanding of Lorentz transformations in special relativity
  • Familiarity with electric and magnetic field concepts
  • Knowledge of Jackson's "Classical Electrodynamics" and its problem sets
  • Basic grasp of vector mathematics and coordinate systems
NEXT STEPS
  • Study Lorentz transformations in detail, focusing on boosts in various directions
  • Explore the relationship between electric and magnetic fields in different reference frames
  • Review problem-solving techniques for electromagnetic field transformations
  • Examine examples of parallel electric and magnetic fields in classical electrodynamics
USEFUL FOR

This discussion is beneficial for physics students, particularly those studying electromagnetism, as well as educators and researchers interested in advanced topics in classical electrodynamics.

egutierrezposse
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This is problem 11.15 of Jackson, Classical Electrodynamics

In a certain reference frame a static, uniform, electric field Eo is parallel to the x axis, and a static, uniform, magnetic induction Bo = 2Eo lies in the xy plane, making an angle theta with the axis. Determine the relative velocity of a reference frame in which the electric and magnetic fields are parallel.


I need the resolution for a general Lorentz transformation (not-only in the z-axis)

Thanks
 
Hello, egutierrezposse. Welcome to PF!

According to forum rules, we need to see some attempt at a solution.

Try to convince yourself that a boost in the z direction will do the trick.
 

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