Examples8.2

# Examples8.2 - 1 Example 1. Let F = ( yze x + xyze x ) i +...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 Example 1. Let F = ( yze x + xyze x ) i + xze x j + xye x k . Show that the integral of F around an oriented simple curve C that is the boundary of a surface S is zero. Solution. By Stokes theorem, Z C F d s = ZZ S ( F ) n dS. We calculate F = i j k x y z yze x + xyze x xze x xye x = [ xe x- xe x ] i- [( y + xy ) e x- ( y + xy ) e x ] j +[( z + xz ) e x- ( z + xz ) e x ] k = 0 . Hence the integrals are zero. Alternatively, one can observe that F = ( xyze x ) and so its integral around any closed curve is zero. 2 Example 2. Find the integral of F ( x,y,z ) = x 2 i + y 2 j- z k around the triangle with vertices (0 , , 0) , (0 , 2 , 0) and (0 , , 3), using Stokes theorem. Solution. In the figure, C is the triangle in question and S is a surface it bounds. By Stokes theorem, Z C F d r = ZZ S ( F ) n dS. Now i j k x y z x 2 y 2- z = 0 i + 0 j + 0 k = 0 ....
View Full Document

## This note was uploaded on 07/19/2010 for the course MA 1C taught by Professor Ramakrishnan during the Spring '08 term at Caltech.

### Page1 / 4

Examples8.2 - 1 Example 1. Let F = ( yze x + xyze x ) i +...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online