Unformatted text preview: region. (Hint : Use Green’s Theorem).
(b) C is a circle, oriented anticlockwise, centred at the origin with radius ε > 0. (Hint :
Green’s Theorem doesn’t apply here (why?). Just evaluate this by parametrizing C
and do what we did last week)
(c) C is a simple closed piecewise smooth curve, oriented anticlockwise, containing
the origin in its inside region. (Hint : Find some creative way of applying Green’s
Theorem.)
3 Does the vector ﬁeld
S j− i
2+ 2 have a potential? (a) The vector ﬁeld is clearly irrotational (i.e. Q − P = 0) away from the
origin and hence the answer to (a) is 0 by Green’s Theorem.
(b) Green’s theorem doesn’t apply here, since the vector ﬁeld is undeﬁned at a...
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This document was uploaded on 02/10/2014.
 Spring '13

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