1 2 show that fz sin z may be regarded as the complex

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: = const, we see that the lines § = constant are at right angle to the equipotentials. Put another way: The lines §= const are parallel to Ô∞ and are therefore lines of force (showing the direction of the force) Looking at the example we just did, the lines of force are given by §(z) = A[Arg(z-c) - Arg(z+c)] = Const In the homework, you will see that these too are circles (except for the one degenerate case when the constant is zero), looking something like magnetic lines of force: (In fact the are the same thing...) Using the Complex Potential to get the Electrostatic Field We know that we can recover the electrostatic field by just taking the gradient of ∞: E = Ô∞ However, ∂∞ ∂∞ ∂∞ ∂§ Ô∞ = “ , ‘=“ ,‘ ∂x ∂y ∂x ∂x ∂∞ ∂§ = -i In complex notation ∂x ∂x = F'(z) where F is the complex potential. Conclusion Conservative Vector Fields and Complex Potentials (Not in Kreyzsig) If E is a conservative field independent of the Ω-coordinate (or in the c...
View Full Document

This document was uploaded on 03/20/2014 for the course MATH 144 at Hofstra University.

Ask a homework question - tutors are online