Given vector field F(7)= ở x7, where T = xi +yj +z k and a is a constant nonzero vector. Let 7.T = d be a plane with the unit normal vector 7. Let L be a simple piecewise smooth oriented closed curve that lies entirely in the plane and let S be a part of the plane bounded by L. The area of S is equal A. The curve L and the surface S are oriented so the normal to the S coincide with n. Use the Stokes' Theorem to find the circlulation of the vector field F over L, that is S, F dT.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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10.
Given vector field F(7)= a x T, where 7 = i +y j +zk and a is a constant
nonzero vector. Let ·T = d be a plane with the unit normal vector . Let L be a simple piecewise
smooth oriented closed curve that lies entirely in the plane and let S be a part of the plane bounded
by L. The area of S is equal A. The curve L and the surface S are oriented so the normal to the S
coincide with ĩ. Use the Stokes' Theorem to find the circlulation of the vector field F over L, that
is f, F dr.
S
Transcribed Image Text:10. Given vector field F(7)= a x T, where 7 = i +y j +zk and a is a constant nonzero vector. Let ·T = d be a plane with the unit normal vector . Let L be a simple piecewise smooth oriented closed curve that lies entirely in the plane and let S be a part of the plane bounded by L. The area of S is equal A. The curve L and the surface S are oriented so the normal to the S coincide with ĩ. Use the Stokes' Theorem to find the circlulation of the vector field F over L, that is f, F dr. S
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