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f = r²e, + 4rzęe + 2zęz

f = r²e, + 4rzęe + 2zęz

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In cylindrical coordinates, a vector function of position is given by f = r?e, + 4rzęe + 2zęz Consider the region of space bounded by a cylinder of radius 2 centered around the z-axis, and having faces at z = 0 and z=1. a) Compute the value of [[S n) dA by direct computation of the surface integral. b) Explain on physical grounds why the component of f in the e, direction does not contribute to the surface integral. c) Determine the value of |[[(V•f)dV by direct computation of the volume integral.
Transcribed Image Text:In cylindrical coordinates, a vector function of position is given by f = r?e, + 4rzęe + 2zęz Consider the region of space bounded by a cylinder of radius 2 centered around the z-axis, and having faces at z = 0 and z=1. a) Compute the value of [[S n) dA by direct computation of the surface integral. b) Explain on physical grounds why the component of f in the e, direction does not contribute to the surface integral. c) Determine the value of |[[(V•f)dV by direct computation of the volume integral.
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