Question

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?

Answer 1

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

Answer 2

dont parametrize it

Answer 3

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

Answer 4

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

Answer 5

-1,-1,-1

Answer 6

whats the vec tor field??

Answer 7

f=<z,x,y>

Answer 8

I cant use divergence theorem right?

Answer 9

im thinking

Answer 10

what with 0 volume.

Answer 11

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

Answer 12

yeah so i need a parametric surface

Answer 13

yeah

Answer 14

thats where im stuck

Answer 15

thats wht i really dunno..;.parametrizing surfaces

Answer 16

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

Answer 17

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

Answer 18

wht u do

Answer 19

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)>

Answer 20

go on.bt watll u do wid d sphere?

Answer 21

Im trying to figure it out i cant remember exactly

Answer 22

i know paramet for cylinders and all bt nt this

Answer 23

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

Answer 24

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

Answer 25

you need 2 parameters for surfaces

Answer 26

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

Answer 27

read it up

Answer 28

uve got t and the vector u here as parameters

Answer 29

u add u the components of i,j,k

Answer 30

kool ill try the eq on that link

Answer 31

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

Answer 32

i think thatll parametrize it

Answer 33

U is an orthognal vector not a parameter

Answer 34

t and r are the parameters

Answer 35

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

Answer 36

can you use polar coords?

Answer 37

you have to integrate over the radius to get a disk

Answer 38

thats how far i cn get at parameterizing it

Answer 39

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

Answer 40

tnx

Answer 41

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

Answer 42

its in 3 space so its in cylindrical

Answer 43

just have z=z be one condition

Answer 44

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

Answer 45

but z does change the disk is tilted in 3 dimentions