Derive Ampere's law from Biot-Savart law?

  • #1
Whyalwaysme
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In Serway physics, ampere derived Ampere's law(integral B dot ds=uI) with work done on the magnetic charge by magnetic field.(similear with E dot ds)
Without using vector calculus, how can derive Ampere's law from Biot-Savart law?
 

Answers and Replies

  • #2
2,811
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Take a wire and calculate its magnetic field. Then calculate the line integral of that magnetic field around a path which encloses a surface that the wire penetrates and show that this will give you the current back. The linearity of Maxwell's equations do the rest.
 

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