Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Cauchy Integral Formula and Electrodynamics

  1. Sep 21, 2004 #1
    Is it possible to solve for an E field from a charge density function using the Cauchy Integral Formulas from complex variables?

    Cauchy Integral Formula about a closed loop in the complex plane
    (Integral[f[z]/ (z-z0)^(n+1)dz = 2 pi i /n! d^n f(z0)/dz ])

    that is the n derivative of f with respect to z evaluated at z0
  2. jcsd
  3. Sep 22, 2004 #2
    If I remember that was a curl type formula and you need a divergence type formula. It may not require math that complicated. It is just that doing the integral might be awkward. In the formula E=Integral (rho/r^2) dr.
  4. Sep 22, 2004 #3
    I was thinking that just like the Gauss's theorem (the surface integral version of the Div[E] = rho/ epsilon) picks out charges which are in effect mathematical singularities, so to the cauchy residue theorem picks out every 1/z of a function.

    Can this similarity be used to solve electrodynamics problems in two dimensions?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook