E & B Fields from Moving Charges: The Magnetic Monopole Mystery

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SUMMARY

The discussion centers on the relationship between electric (E) and magnetic (B) fields as observed from different frames of reference, particularly in the context of a negative line charge on a rod. When stationary with respect to the rod, an observer detects an E field, while a moving observer perceives a B field. The invariance of the expression E²/c² - B² is highlighted, indicating that a stationary magnetic monopole, if it exists, would yield a negative value for this expression, suggesting a fundamental difference between E and B fields. The conversation also touches on the implications for the existence of magnetic monopoles in relation to electron behavior.

PREREQUISITES
  • Understanding of electromagnetic fields, specifically E and B fields
  • Familiarity with the concept of frames of reference in physics
  • Knowledge of the electromagnetic tensor and its properties
  • Basic grasp of special relativity, particularly Lorentz transformations
NEXT STEPS
  • Research the properties of the electromagnetic tensor and its implications for E and B fields
  • Study the concept of magnetic monopoles and their theoretical existence
  • Explore Lorentz transformations and their effects on electric and magnetic fields
  • Learn about the invariance of physical quantities in different frames of reference
USEFUL FOR

Physicists, students of electromagnetism, and anyone interested in the theoretical aspects of magnetic monopoles and the interplay between electric and magnetic fields.

cragar
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Lets say I have a negative line charge on a long thin rod, if I am at rest with respect to that rod I will see an E field. But If I am moving with respect to that rod I will see a B field. So why are people looking for magnetic monopoles, If B fields are E fields in disguise, wouldn't the electrons need to show magnetic monopoles if they existed?
 
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hi cragar! :smile:
cragar said:
Lets say I have a negative line charge on a long thin rod, if I am at rest with respect to that rod I will see an E field. But If I am moving with respect to that rod I will see a B field.

yes, but it's only a tiny-weeny B field …

it's still mostly an E field :wink:​

E2/c2 - B2 is invariant (the same in all frames), so since it's positive for the stationary rod, it's always positive

(if the speed is tanhu, then |E| = cE0coshu and |B| = E0sinhu)

similary, a stationary magnetic monople (if it exists) will have E = 0, and so E2/c2 - B2 will be negative, in that and any other frame …

there's no frame transformation that will turn pure E into pure B :smile:​
 
Last edited:
I though it was E(dot)B that was invariant . Or is your way also equivalent. We can have frames where there is pure B then some E and B, but that probably doesn't help my case.
 
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