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?

- anonymous

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- anonymous

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

- anonymous

dont parametrize it

- anonymous

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

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## More answers

- anonymous

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

- anonymous

-1,-1,-1

- anonymous

whats the vec tor field??

- anonymous

f=

- anonymous

I cant use divergence theorem right?

- anonymous

im thinking

- anonymous

what with 0 volume.

- anonymous

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

- anonymous

yeah so i need a parametric surface

- anonymous

yeah

- anonymous

thats where im stuck

- anonymous

thats wht i really dunno..;.parametrizing surfaces

- anonymous

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

- anonymous

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

- anonymous

wht u do

- 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

go on.bt watll u do wid d sphere?

- anonymous

Im trying to figure it out i cant remember exactly

- anonymous

i know paramet for cylinders and all bt nt this

- 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

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

- anonymous

you need 2 parameters for surfaces

- 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

read it up

- anonymous

uve got t and the vector u here as parameters

- anonymous

u add u the components of i,j,k

- anonymous

kool ill try the eq on that link

- anonymous

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

- anonymous

i think thatll parametrize it

- anonymous

U is an orthognal vector not a parameter

- anonymous

t and r are the parameters

- anonymous

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

- anonymous

can you use polar coords?

- anonymous

you have to integrate over the radius to get a disk

- anonymous

thats how far i cn get at parameterizing it

- anonymous

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

- anonymous

tnx

- anonymous

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

- anonymous

its in 3 space so its in cylindrical

- anonymous

just have z=z be one condition

- anonymous

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

- anonymous

but z does change the disk is tilted in 3 dimentions

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