Understanding Z = -sin(t) in Stokes Theorem: A Simple Explanation

In summary, Stokes theorem problem involves calculating the circulation of a vector field around a closed curve or surface. Its purpose is to provide a relationship between line integrals and surface integrals. The conditions for applying Stokes theorem are that the vector field must be continuously differentiable and the surface or curve must be smooth and orientable. To solve a Stokes theorem problem, one must determine if the given conditions are met, calculate the line and surface integrals, and apply the theorem to relate the two. Real-world applications of Stokes theorem include fluid mechanics, electromagnetism, and differential geometry.
  • #1
Miike012
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I am wondering why z = -sin(t) and not sin(t)
 

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  • #2
nevermind i think i know. I think its because as you rotate around the circle in the counter clockwise direction you go from the x-axis to the negative z-axis.
 

What is Stokes theorem problem?

Stokes theorem problem is a mathematical concept that involves calculating the circulation of a vector field around a closed curve or surface.

What is the purpose of Stokes theorem?

The purpose of Stokes theorem is to provide a relationship between line integrals and surface integrals. It allows us to calculate surface integrals by evaluating line integrals over a closed curve.

What are the conditions for applying Stokes theorem?

The conditions for applying Stokes theorem are that the vector field must be continuously differentiable and the surface or curve must be smooth and orientable.

How do you solve a Stokes theorem problem?

To solve a Stokes theorem problem, you need to first determine if the given conditions are met. Then, calculate the line integral over the closed curve and the surface integral over the smooth surface. Finally, apply Stokes theorem to relate the two integrals and solve for the desired value.

What are some real-world applications of Stokes theorem?

Stokes theorem has applications in various fields such as fluid mechanics, electromagnetism, and differential geometry. It is used to calculate fluid flow around a closed loop, determine the flux of a magnetic field through a surface, and study the curvature of a surface, among others.

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