Ampere's law - single or double integral?

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SUMMARY

The discussion centers on the representation of flux in the context of Ampere's law, specifically questioning why it is expressed as a single integral rather than a double integral. The key point is that while the flux can be calculated using a single integral, it can also be transformed into a double integral when integrating over an area, such as using dA = dxdy. This flexibility in representation is crucial for understanding the application of Ampere's law in various scenarios.

PREREQUISITES
  • Understanding of vector calculus
  • Familiarity with Ampere's law
  • Knowledge of surface integrals
  • Basic proficiency in mathematical notation
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  • Explore the concept of surface integrals in vector calculus
  • Study the applications of Ampere's law in electromagnetic theory
  • Learn about the transformation of integrals in multivariable calculus
  • Investigate the relationship between flux and electric fields
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kasse
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Flux = Int B dA

Why isn't this written as a double integral when we antidifferentiate over an areal?
 
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Forget about Ampere.
 
When you actually go to calculate the flux you can change it to a double integral, if needed: perhaps dA = dxdy.
 

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