Trouble with Biot-Savart Law: Instant Effects & Ampere-Maxwell Law

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SUMMARY

The Biot-Savart Law applies specifically in magnetostatics, where currents remain constant over time. This law is often compared to Coulomb's Law, which is applicable in electrostatics with constant charge densities. Both laws are special cases of the Jeffimenko equations, which provide a comprehensive framework for understanding electric and magnetic fields generated by varying charges. The discussion clarifies that the Biot-Savart Law does not account for instantaneous electromagnetic effects over distance, a limitation that can be addressed using the Ampere-Maxwell Law.

PREREQUISITES
  • Understanding of Biot-Savart Law in magnetostatics
  • Familiarity with Coulomb's Law in electrostatics
  • Knowledge of the Ampere-Maxwell Law
  • Basic concepts of the Jeffimenko equations
NEXT STEPS
  • Study the derivation and applications of the Biot-Savart Law
  • Explore the Ampere-Maxwell Law and its implications for dynamic systems
  • Read about the Jeffimenko equations and their role in electromagnetism
  • Consult Griffith's "Introduction to Electrodynamics" for detailed explanations
USEFUL FOR

Students of physics, electrical engineers, and anyone seeking to deepen their understanding of electromagnetic theory and the relationships between electric and magnetic fields.

LeoPedranjo
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Guys, I'm having trouble with some concepts on the Biot-Savart Law. Lots of texts compare this law with Coulomb Law, but doesn't affirm that B-S is only applicable on a static case (constant current). What are the real physical conditions in which Biot-Savart Law can be directly applied? Does it covers the instant eletromagnetic effects with the distance (as the Coulomb Law doesn't)?
Also, to surpass the instant effects over distance, could I aplly the Ampere-Maxwell law?

Thanks!
 
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Long story short, The Biot-savart law applies in magnetostatics, where currents are constant in time.
Similarly, Coulomb's law, applies in electrostatics, where charge densities are constant in time (though individual charges may be moving)

These laws are special cases of what are known as the Jeffimenko equations, which completely describe the electric and magnetic field generated from an arbitrarily changing collection of charges (both Wikipedia and Griffith's E&M book have good introductions).
 
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