Question

CAN SOMEONE HELP WITH A FLUX INTEGRAL?

Answer 1

F=(x^2y,-xy^2,z) around x^2+y^2+z^2=1

Answer 2

if they were both vector it would be much easier, lol

Answer 3

huh? i havent seen that form yet?

Answer 4

I just did those for hw last week ,trying to recall it

Answer 5

alright take you time

Answer 6

any progress im?

Answer 7

just thought of something; checking it

Answer 8

ok

Answer 9

let's do simplest case and build up from there

sphere has radius of 1


field point radially so

F . dA

F dA cos(0)
since they are same direction
F * 4 Pi r^2

E=a/r^2
=a/r^2* 4 Pi r^2

flux = 4 a pi

\[\int \int E .dA\]


let's try to use it for this problem

Answer 10

wait whrere did the 4 come from?

Answer 11

this is a physics stand point huh?

Answer 12

yeah

Answer 13

I am building up from easy problem

Answer 14

ok lets try

Answer 15

this is what i think
\[\int\limits_{}^{}\int\limits_{}^{}\int\limits_{}^{} ▼◦(x^2y,-xy^2,z)dV\]

which equals tripple integral of 1 but i dont know if thats right and 1||R||=1

Answer 16

does that work with you E.dA?

Answer 17

I think surface integral is way to go

Answer 18

hmm alright i think its right

Answer 19

\[\left\{x^2 y,-x y^2,z\right\}.\left\{\frac{2 x}{\sqrt{4 x^2+4 y^2+4 z^2}},\frac{2 y}{\sqrt{4 x^2+4 y^2+4 z^2}},\frac{2 z}{\sqrt{4 x^2+4 y^2+4 z^2}}\right\}\]

=\[\frac{x^3 y-x y^3+z^2}{\sqrt{x^2+y^2+z^2}}\]

\[\int \frac{x^3 y-x y^3+z^2}{\sqrt{x^2+y^2+z^2}} \, dA\]

\[4\pi \sqrt{x^2+y^2+z^2} \left(x^3 y-x y^3+z^2\right)\]

Answer 20

that looks bad

Answer 21

yeah 1||R|| which R=4/3pir^3
which r=1 4/3(pi) i think this is the right answer