anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
I found that it lies in the plane -x-y-z=3
anonymous
  • anonymous
dont parametrize it
anonymous
  • anonymous
should i take the intersection between this plane and a sphere centered at 111

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More answers

anonymous
  • anonymous
find a vec tor normal to it, with magnitude of the area of the disk
anonymous
  • anonymous
-1,-1,-1
anonymous
  • anonymous
whats the vec tor field??
anonymous
  • anonymous
f=
anonymous
  • anonymous
I cant use divergence theorem right?
anonymous
  • anonymous
im thinking
anonymous
  • anonymous
what with 0 volume.
anonymous
  • anonymous
thats whts confusing me..no i dont think divergence thm is applicabe..old way then
anonymous
  • anonymous
yeah so i need a parametric surface
anonymous
  • anonymous
yeah
anonymous
  • anonymous
thats where im stuck
anonymous
  • anonymous
thats wht i really dunno..;.parametrizing surfaces
anonymous
  • anonymous
i can find the intersection between the sphere and a plane but its an ugly integral
anonymous
  • anonymous
I know theres another way to do it using tangents to the normal but i cant remember
anonymous
  • anonymous
wht u do
anonymous
  • 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
anonymous
  • anonymous
go on.bt watll u do wid d sphere?
anonymous
  • anonymous
Im trying to figure it out i cant remember exactly
anonymous
  • anonymous
i know paramet for cylinders and all bt nt this
anonymous
  • 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
anonymous
  • anonymous
check this out: http://www.physicsforums.com/showthread.php?t=123168
anonymous
  • anonymous
you need 2 parameters for surfaces
anonymous
  • 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
anonymous
  • anonymous
read it up
anonymous
  • anonymous
uve got t and the vector u here as parameters
anonymous
  • anonymous
u add u the components of i,j,k
anonymous
  • anonymous
kool ill try the eq on that link
anonymous
  • anonymous
u get x,y,z in terms of t and u
anonymous
  • anonymous
i think thatll parametrize it
anonymous
  • anonymous
U is an orthognal vector not a parameter
anonymous
  • anonymous
t and r are the parameters
anonymous
  • anonymous
r is the radius mate...u is the parametric vector from the centre to that point and n is the orthogonal vector
anonymous
  • anonymous
can you use polar coords?
anonymous
  • anonymous
you have to integrate over the radius to get a disk
anonymous
  • anonymous
thats how far i cn get at parameterizing it
anonymous
  • anonymous
i g2g.. i learnt a lot thru this discusion..thnx..hope u get it
anonymous
  • anonymous
tnx
anonymous
  • anonymous
polar is the way to go, I'm not sure what him1618 meant
anonymous
  • anonymous
its in 3 space so its in cylindrical
anonymous
  • anonymous
just have z=z be one condition
anonymous
  • anonymous
if z doesn't vary, well i guess cylindrical still applies, anyway the jacobian is still r
anonymous
  • anonymous
but z does change the disk is tilted in 3 dimentions

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