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Let Mbe the intersection of 3,2 + z2 = 23nd a: = 1 + Z2, and let C be the portion of M in the region with z 3 0 between the points (2, —1, —1) and (17 —ﬂ, 0). (a) Find a parametrization for 0, clearly indicating its domain. What are the starting and ending points associated with your parametrization?

October 23, 2020/in Feeds /by admin

Let Mbe the intersection of 3,2 + z2 = 23nd a: = 1 + Z2, and let C be the portion of M in the region with z 3 0 between the points
(2, —1, —1) and (17 —ﬂ, 0). (a) Find a parametrization for 0, clearly indicating its domain. What are the starting and ending points associated with your parametrization? Suggestion: use polar coordinates to parametrize y and 2.] (b) Show that the work done by the force
F(Eiy?z) = (1’ —32, z)
to move our particle along 0 from (1, —‘/§J 0) to (2, —1, —1) is W = 37r/4. (c) Suppose 0 models a piece of wire with charge density given by u(:z:,y,z) = 3\/§(ysz _ yZ3). Show that the total charge on this piece of wire is Q=3\/§—1.