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

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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anawer all the question

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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