Instead we just calculate as usual c can be

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: point (the origin) in the interior domain of C . Instead we just calculate as usual. C can be prametrised as = ε cos = ε sin ∈ [0 2π ] We get = −ε sin = ε cos and − 2+ C 2π 2 = 0 ε cos ε sin − ε sin (−ε sin ) ε2 2π = 1 = 2π 0 (c) Let Cε be a circle with radius ε oriented anticlockwise centred at the origin, where the radius ε is small enough for Cε to be contained in the interior region of C . Let D be the region inside C but outside Cε . The given vector field satisfies the conditions of Green’s theorem on the region D, where we also have Q − P = 0, so by Green’s theorem we have C j− i − +2 2 Cε j− i = +2 2 (Q − P ) D = 0 =0 D But in part (b) we saw that Cε hence C j− i = 2π...
View Full Document

This document was uploaded on 02/10/2014.

Ask a homework question - tutors are online