Why Does j.ds Have Closed Integral on Electromagnetics Equation?

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SUMMARY

The discussion centers on the necessity of a closed integral in the context of the electromagnetics equation involving current density (j) and surface area (ds). It emphasizes that the closed integral is essential for representing the continuity equation, which accounts for charge conservation within a defined region of space. The closed surface integral captures the total current flowing through the boundary of that region, reflecting the principle that charge cannot be created or destroyed.

PREREQUISITES
  • Understanding of electromagnetics principles, specifically the continuity equation.
  • Familiarity with vector calculus, particularly surface integrals.
  • Knowledge of current density (j) and its role in charge conservation.
  • Basic comprehension of closed surfaces in three-dimensional space.
NEXT STEPS
  • Study the derivation and applications of the continuity equation in electromagnetics.
  • Explore vector calculus techniques for evaluating surface integrals.
  • Learn about Maxwell's equations and their implications for charge conservation.
  • Investigate the physical significance of closed surfaces in electromagnetic theory.
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Students and professionals in physics, electrical engineering, and applied mathematics who are studying electromagnetics and charge conservation principles.

bhanesh
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Why j.ds has ' closed integral ' on below equation

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I think this is some kind of continuity equation.Its considering a region of space with some charge inside it.Because charge can't be created or destroyed,the only thing which can cause the amount of charge to change is a current and so we should have a surface integral of current density.But because we're interested in a region of space,the surface is the one enclosing that region which is of course closed.
 

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