Purchase Solution

Stokes theorem

Not what you're looking for?

Ask Custom Question

Given the vector field F=3yi + (5-2x)j + ((z^2)-2)k find

a) Div F
b) Curl F
c) The surface integral of the normal component of curl F over the open hemispherical surface (x^2)+(y^2)+(z^2)=4 above the xy plane.

* Hint: by a double application of Stokes theorem, part c can be reduced to a triviality

Purchase this Solution
Solution Summary

Stokes theorem is applied.

Solution Preview

Hello and thank you for posting your question to Brainmass!

The solution is attached below in two files. ...

Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Probability Quiz

Some questions on probability

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

View More Free Quizzes
Related BrainMass Solutions

  • Connections among Green's, Stokes' and Divergence theorems

    35214 Green's, Divergence and Stokes theorems Describe in 5-15 lines the links and connections among Green's theorem in all forms, Stokes' theorem and the Divergence theorem.

  • Stokes Theorem

    137292 Stokes Theorem Stokes Theorem. See attached file for full problem description. Use Stokes Theorem to evaluate.... Please see the attached file. This provides an example of using Stokes Theorem.

  • Green's Theorem and Stokes' Theorem

    35016 Green's Theorem and Stokes' Theorem Using Green's Theorem and Stokes' Theorem respectively, calculate the given line integrals.

  • Stokes and Gauss' Theorem

    (Hint: This is similar to the previous problem, but using Gauss' theorem instead of Stokes' theorem.) Please see the attached file. This Solution contains calculations to aid you in understanding the Solution to these questions.

  • Stokes Theorem, Curl and Positively Oriented Hemisphere

    42947 Stokes Theorem, Curl and Positively Oriented Hemisphere 7) Use Stoke's Theorem to evaluate curl F*dS S is the hemisphere oriented in the direction of the positive x-axis. 8) Use Stokes Theorem to evaluate C is the boundary of the part

  • application of Stokes Theorem

    127063 Applications of the Stokes Theorem Stokes Theorem.

  • Stokes theorem to calculate the surface integral of the curl

    The solution shows detailed steps of using Stokes theorem to calculate the surface integral of the curl.

  • application of Stokes' theorem

    108973 Stokes' Theorem : Curls and Surface Integrals Let F = (2x, 2y, 2x + 2z). Use Stokes' theorem to evaluate the integral of F around the curve consisting of the straight lines joining the points (1,0,1), (0,1,0) and (0,0,1).

  • Proof of Fixed Point Theorem using Stokes Theorem and Analysis

    18931 Proof of Fixed Point Theorem using Stokes Theorem and Analysis Prove that if D is the closed disc |x|  1 in R2, then any map f 2 C2[D ! D] has a fixed point: f(x) = x. The proof is by contradiction, and uses Stokes theorem.

View More Related Solutions