Question

Calculate the flux of the vector field F = 3i + 6j through a square of side 4 lying in the plane x + y + z = 15 oriented away from the origin.

Answer 1

\[flux=F.A\]
so first try to find out the area vector

Answer 2

so i can say that the an upward normal vector is\[A_u=\hat{i}+\hat{j}+\hat{k}\]

Answer 3

so the unit normal vector will be
\[A_{UN}=\frac{ \hat{i}+\hat{j}+\hat{k} }{ \sqrt{1^2+1^2+1^2} }=\frac{ \hat{i}+\hat{j}+\hat{k} }{ \sqrt{3} }\]

Answer 4

ok?

Answer 5

so the area vector will be\[A_v=A_{UN}*4=\frac{ 4(\hat{i}+\hat{j}+\hat{k}) }{ \sqrt{3} }\]

Answer 6

so \[flux=F.A_v\]

Answer 7

so do a little dot product

Answer 8

what would i do with the =15?

Answer 9

\[flux=(3 \hat{i}+4 \hat{j})*\frac{ 4(\hat{i}+\hat{j}+\hat{k}) }{ \sqrt{3}}\]

Answer 10

15 is just a constant

Answer 11

so just (12+16+4)/square root(3)

Answer 12

why 12+16+14

Answer 13

so 32/square root(3)

Answer 14

wait just (12+16)/square root(3)

Answer 15

\[Flux=\frac{ 4 }{ \sqrt{3} }*(\hat{i}+\hat{j}+\hat{k})(3 \hat{i}+4\hat{j})=\frac{ 4 }{ \sqrt{3} }*(3+4)=\frac{ 28 }{ \sqrt{3} }\]

Answer 16

yes that should be it !!

Answer 17

matches your answer?

Answer 18

got it thanks

Answer 19

:)

Answer 20

yw!!

Answer 21

wait

Answer 22

we did it wrong

Answer 23

it should be (3i+6j) * 4/square root(3) (i+j+k) right?

Answer 24

@sidsiddhartha

Answer 25

oohh my bad sorry

Answer 26

then\[36/\sqrt{3}\]
right?

Answer 27

yeah but its making it wrong :(

Answer 28

marking it wrong

Answer 29

what are we doing wrong?

Answer 30

i dont know @perl can u check this out?

Answer 31

ok u can put a minus ahead of the answer and check it again but not sure it will work or not

Answer 32

no it didnt work

Answer 33

as the vector is oriented away from the origin

Answer 34

it also marking wrong -36/square root(3)

Answer 35

try \[12\sqrt{3}\]

Answer 36

does "square of side 4 lying in the plane" has something to do with it?

Answer 37

no the 12 didnt work

Answer 38

I only have one more try left

Answer 39

ok let me tag experts @Kainui

Answer 40

@ganeshie8

Answer 41

thanks

Answer 42

what about (3i+6j)*16(i+j+k)/square root(3)

Answer 43

because of the square of side 4

Answer 44

yes i missed it

Answer 45

you think so?

Answer 46

yes area=16

Answer 47

so 144/square root(3)

Answer 48

yes it should be okay !!

Answer 49

NO :( I got it wrong

Answer 50

so what do you think the answer should be?

Answer 51

can you help me with this one

Answer 52

@sidsiddhartha

Answer 53

what were the options for the last one?

Answer 54

@SithsAndGiggles

Answer 55

for the flux? it didn't have options

Answer 56

can you help me with the screen shot that i post? please :)

Answer 57

done with the main question right ?

Answer 58

no the answer is'nt correct she says, can u check it @ganeshie8

Answer 59

it was not the current density. I got it wrong. ;( what should the right answer be? @ganeshie8

Answer 60

yeah I would like to know what we did wrong