Register to reply 
Cauchy's Integral Formula and Ampere's Law  Any Connection?by brandon_1892
Tags: ampere's law complex 
Share this thread: 
#1
Feb513, 05:31 PM

P: 1

I know how, by Amp[itex]\grave{e}[/itex]re's Law for the loop integral of a magnetic field, $$\oint_C \textbf B \cdot d \textbf s = \mu_0 I$$ and this is zero when there is no current enclosed in the loop; there is a nonzero result when there is a current.
With Cauchy's Integral Theorem, if a function is analytic on and in the loop integrated over, $$\oint_C f(z) dz = 0$$; otherwise there may be a nonzero result. Since essentially the magnetic field approaches infinity right in the current, I thought maybe Ampere's Law is an instance of Cauchy's Integral Formula/Theorem; when there is no current enclosed, the magnetic field has no such center, so all of it would be analytic. Is this an actual connection, then? 


Register to reply 
Related Discussions  
Using Cauchy integral formula to compute real integral?  Calculus & Beyond Homework  3  
Cauchy Integral Formula  Calculus & Beyond Homework  1  
The Cauchy Integral Formula  Calculus & Beyond Homework  6  
Cauchy's integral formula  Calculus & Beyond Homework  8  
Is Cauchy's integral formula applicable to this type of integral?  Calculus & Beyond Homework  4 