Cauchy Integral Formula and Electrodynamics

  • Thread starter sinyud
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  • #1
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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
 

Answers and Replies

  • #2
133
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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.
 
  • #3
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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?
 

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