Question

Calculate the flux of the vector field through the surface
F=i +2j through a sphere of radius 3 at the origin

Answer 1

perhaps we could apply divergence theorem ...

Answer 2

hmmm that is next chapter

Answer 3

you have the answer??

Answer 4

nope not this time

Answer 5

looks like we have to find tangential areal vector first.

Answer 6

like shld i show u a previous example and how it was solved?

Answer 7

yeah that would be helpful.

Answer 8

ok so F=2i +3jthrough a disk of radius 5 in th eplane y=2oriented in the direction of increasing y

Answer 9

Answer: area of disk is 25pi
Flux = (21+3j)*25pij = 75pi

Answer 10

ummmm so?

Answer 11

HA ... that was so nice and easy

You multiplied Field (only y component) with area ...

Answer 12

right but what do u do here

Answer 13

when do i choose which component to use?

Answer 14

we know the area ... we don't know the component.

Answer 15

right

Answer 16

well in the example we knew the component and the area

Answer 17

Formula was supposed to be
surface integration of F.ds <--- and this ds is areal vector

somehow I have a feeling that the answer will be zero.

Answer 18

hmmm i may have the answer

Answer 19

since F is a constant vector field the flux through a closed surface is 0
the flux that enters one side exits the other

Answer 20

yeah ... but how to prove it ... without using divergence theorem.

Answer 21

hmmm maybe i just need a better explanation or a diagram

Answer 22

It would be something like this ... esp in case of sphere

r^2 = x^2 + y^2 + z^2
Normal vector = del (r^2 - (x^2 + y^2 + z^2)) = -2xi - 2yj - 2zk

the normal unit vectors are, 1/sqrt(3), 1/sqrt(3), 1/sqrt(3)

Answer 23

sorry
x/sqrt(3), y/sqrt(3), z/sqrt(3)

Answer 24

Oo ... i forgot to put x's and y's down there
x/rsqrt(3), y/rsqrt(3), z/rsqrt(3) , and since we already know r=3, we have

x/3sqrt(3), y/3sqrt(3), z/3sqrt(3)

Answer 25

ugghhh how did u get this equation?

Answer 26

taking gradient of the equation of circle.

Answer 27

ohhhh ok never did that b4

Answer 28

really??? I thought you do these http://en.wikipedia.org/wiki/Del first. They are basics.

Answer 29

hahahaha idk nemore

Answer 30

okay still we can take standard unit normal vector as (x/3sqrt(3), y/3sqrt(3), z/3sqrt(3) and integrate it all over the surface of sphere.

Answer 31

hey dont drive urself crazy. I needed the answer that i told u i guess iw ont prove it

Answer 32

<(i +2j), (x/3sqrt(3), y/3sqrt(3), z/3sqrt(3))> = x/3sqrt(3) + 2y/3sqrt(3)

well, if you say so then ..

Answer 33

like ill just copy the answer like i am tooo tired to think like its 3 30 am here lol

Answer 34

THANKS EXPERIMENT u r always a savior. like u never run off on me u always stay till i figure it out

Answer 35

No ... it's rather I'm trying to learn things. anyway good night.

Answer 36

Well thanks for ur time i really appreciate it