A Magnetic Misconception on Divergence 0/Closed Field Lines?

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SUMMARY

The discussion addresses the misconception that closed magnetic field lines imply zero net work done by magnetic forces. It clarifies that while magnetic fields exhibit divergence zero, this does not universally apply to work done on electric charges. The conversation draws parallels between magnetic and electric fields, emphasizing that closed field lines in electric fields, such as those around an electric dipole, can indeed perform work on charges. This distinction is crucial for understanding the dynamics of both magnetic and electric fields.

PREREQUISITES
  • Understanding of Maxwell's equations
  • Familiarity with magnetic field concepts
  • Knowledge of electric field behavior
  • Basic principles of electromagnetism
NEXT STEPS
  • Study Maxwell's equations in detail
  • Explore the concept of divergence in vector fields
  • Investigate the work done by electric fields on charges
  • Examine the behavior of electric dipoles in electric fields
USEFUL FOR

Students and professionals in physics, particularly those studying electromagnetism, as well as educators seeking to clarify misconceptions about magnetic and electric fields.

walkeraj
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Question: Can we ultimately atttribute no work or net zero work done by a magnetic force to the closed magnetic field lines that results in Divergence zero of a magnetic field? That is, is it a misconception to say that closed magnetic field lines imply magnetic force will always result in no net work?

(I meant misconception on my part not theory.)

Edit: Why misconception? Now switch to electric field. The field lines between two opposite electric test charges are also closed and resemble that of a bar magnet, though electric in nature. Does it hold? Is it enough to say that since the field lines are closed between the two test charges that no net work can ever be done?
 
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Work done by a magnetic force on what ? Electric charge ?
 
Electric charge is all I can see (thinking back to Griffith's book).
 
Consider the electric field of an idealized electric dipole. It has only closed field lines, but it can do work on a charge.
 
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