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Stokes' theorem is an equality relationship between the surface integral over a surface S and line integral around the boundary curve C with the curl of vector field F involved. This theorem is given by fF•dr = {[, curlF.ndS. where z represents the line and n defines the unit nomal vector to the surface. (a) State two main conditions for the Stokes" theorem. (b) For the following figure, assume that surface S has upward orientation. Can Stok applied te the imra? Evelai

Stokes' theorem is an equality relationship between the surface integral over a surface S and line integral around the boundary curve C with the curl of vector field F involved. This theorem is given by fF•dr = {[, curlF.ndS. where z represents the line and n defines the unit nomal vector to the surface. (a) State two main conditions for the Stokes" theorem. (b) For the following figure, assume that surface S has upward orientation. Can Stok applied te the imra? Evelai

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Vectors In Two And Three Dimensions
Section9.FOM: Focus On Modeling: Vectors Fields
Problem 11P
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Stokes' theorem is an equality relationship between the surface integral over a surface S and line integral around the boundary curve C with the curl of vector field F involved. This theorem is given by $.F dr = f[, curlF .ndS. where r represents the line and n defines the unit nomal vector to the surface. (a) State two main conditions for the Stokes' theorem. (b) For the following figure, assume that surface S has upward orientation. Can Stokes' theorem be applied to the figure? Explain your answer. S (2 =1+ x) (c) The flux inside the 3-dimensional (3D) hemisphere of x +y° +z? =25 with planes of 220 is represented by the vector F = 2i +2x j+yk. i) Sketch the diagram of the hemisphere with identify radius. ii) By using Stokes' theorem, evaluate fF - dr.
Transcribed Image Text:Stokes' theorem is an equality relationship between the surface integral over a surface S and line integral around the boundary curve C with the curl of vector field F involved. This theorem is given by $.F dr = f[, curlF .ndS. where r represents the line and n defines the unit nomal vector to the surface. (a) State two main conditions for the Stokes' theorem. (b) For the following figure, assume that surface S has upward orientation. Can Stokes' theorem be applied to the figure? Explain your answer. S (2 =1+ x) (c) The flux inside the 3-dimensional (3D) hemisphere of x +y° +z? =25 with planes of 220 is represented by the vector F = 2i +2x j+yk. i) Sketch the diagram of the hemisphere with identify radius. ii) By using Stokes' theorem, evaluate fF - dr.
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