Generalized Ohm's Law: Current Density & Capacitance

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SUMMARY

The discussion centers on the Generalized Ohm's Law, specifically addressing the divergence of current density in continuous loops without capacitors. Participants assert that while the divergence of current density is typically accepted as zero in such scenarios, the Generalized Ohm's Law suggests otherwise. The conversation highlights the necessity for the law to accommodate capacitors and other current sources or sinks, indicating that a non-vanishing divergence term may be essential for a comprehensive understanding of the law's applicability.

PREREQUISITES
  • Understanding of Generalized Ohm's Law
  • Familiarity with current density concepts
  • Knowledge of capacitor behavior in electrical circuits
  • Basic principles of divergence in vector calculus
NEXT STEPS
  • Research the implications of divergence in current density in various circuit configurations
  • Study the role of capacitors in electrical circuits and their effect on current flow
  • Explore advanced topics in plasma physics related to current density
  • Examine mathematical treatments of Generalized Ohm's Law in different physical contexts
USEFUL FOR

Electrical engineers, physicists, and students studying circuit theory and plasma physics will benefit from this discussion, particularly those interested in the nuances of current density and its implications in various electrical systems.

mertcan
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initially my attachment/picture has been cut off that link http://sun.stanford.edu/~sasha/PHYS780/PLASMA_PHYSICS/phys780_2014_l13.pdf page 6

Also I would like to put into words that divergence of current density is accepted as 0 in continuous loop( no capacitors exist...). But if you look at the generalized ohm law divergence of current density seems to be not zero. How is that possible?
 

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mertcan said:
Also I would like to put into words that divergence of current density is accepted as 0 in continuous loop( no capacitors exist...). But if you look at the generalized ohm law divergence of current density seems to be not zero.
Wouldn't the generalized law need to work for capacitors (or other current sources and sinks) in order to be general? In those cases, you would need a term with non-vanishing divergence.
 

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