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Unformatted text preview: a 2 b. Curl (use formula from cylindrical coordinates): ~ ~ F = + 2 z. c. The elemental area is ~ d a = r d d r z, so x A ( ~ ~ F) ~ d a = Z a Z 2 2 r d r d = 2 a 2 d. From (a) and (c), we have shown that I ~ F ~ d s = x A ( ~ ~ F) ~ d a = 2 a 2 . e. For convenience, express the curl in spherical coordinates: ~ ~ F = +2cos r. On the spherical surface, the elemental area is ~ d a = a 2 sin d d r, so I ~ F ~ d s = Z / 2 Z 2 2 a 2 cos sin d d = 2 a 2 Although the surface is dierent than for part (c), the answer is the same! (Stokes Theorem.) CORNELL UNIVERSITY c WES SWARTZ (09/8/12) 11...
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This note was uploaded on 01/16/2010 for the course ECE 3030 at Cornell.