## anonymous 5 years ago I need to find the flux through a disk of radius 1 centered at (1,1,1) with its normal pointing towards the origin. How do i parameterize this disk?

1. anonymous

I found that it lies in the plane -x-y-z=3

2. anonymous

dont parametrize it

3. anonymous

should i take the intersection between this plane and a sphere centered at 111

4. anonymous

find a vec tor normal to it, with magnitude of the area of the disk

5. anonymous

-1,-1,-1

6. anonymous

whats the vec tor field??

7. anonymous

f=<z,x,y>

8. anonymous

I cant use divergence theorem right?

9. anonymous

im thinking

10. anonymous

what with 0 volume.

11. anonymous

thats whts confusing me..no i dont think divergence thm is applicabe..old way then

12. anonymous

yeah so i need a parametric surface

13. anonymous

yeah

14. anonymous

thats where im stuck

15. anonymous

thats wht i really dunno..;.parametrizing surfaces

16. anonymous

i can find the intersection between the sphere and a plane but its an ugly integral

17. anonymous

I know theres another way to do it using tangents to the normal but i cant remember

18. anonymous

wht u do

19. anonymous

well the disk lies in the plane -x-y-z=3 and theres a sphere with rad 1 cestered at (1.1.1) of the form <rcos(theta)sin(phi), rsin(theta)sin(phi), rcos(phi)>

20. anonymous

go on.bt watll u do wid d sphere?

21. anonymous

Im trying to figure it out i cant remember exactly

22. anonymous

i know paramet for cylinders and all bt nt this

23. anonymous

Using vectors, generally if t is the parameter then and point P on the circle is given by; LaTeX Code: P = R\\cos(t) \\vec{u} + R\\sin(t) \\;\\;\\vec{n}\\times\\vec{u} + c

24. anonymous

check this out: http://www.physicsforums.com/showthread.php?t=123168

25. anonymous

you need 2 parameters for surfaces

26. anonymous

go down to the post where it writes a parametric eqn for a circle in 3d..our surface is actually a circle at some angle

27. anonymous

28. anonymous

uve got t and the vector u here as parameters

29. anonymous

u add u the components of i,j,k

30. anonymous

kool ill try the eq on that link

31. anonymous

u get x,y,z in terms of t and u

32. anonymous

i think thatll parametrize it

33. anonymous

U is an orthognal vector not a parameter

34. anonymous

t and r are the parameters

35. anonymous

r is the radius mate...u is the parametric vector from the centre to that point and n is the orthogonal vector

36. anonymous

can you use polar coords?

37. anonymous

you have to integrate over the radius to get a disk

38. anonymous

thats how far i cn get at parameterizing it

39. anonymous

i g2g.. i learnt a lot thru this discusion..thnx..hope u get it

40. anonymous

tnx

41. anonymous

polar is the way to go, I'm not sure what him1618 meant

42. anonymous

its in 3 space so its in cylindrical

43. anonymous

just have z=z be one condition

44. anonymous

if z doesn't vary, well i guess cylindrical still applies, anyway the jacobian is still r

45. anonymous

but z does change the disk is tilted in 3 dimentions