Question

Let F = (ax + by + 10z) i  + (x + cz) j  + (7y + mx) k 
where a, b,c, and m are constants.

a) Suppose that the flux of F through any closed surface is 0. Which of the constants can be determined?


a

m

b

c

b) Suppose instead that the circulation of
F around any closed curve is 0. Find the value of each.

b =
c =
m =

Answer 1

@myininaya can you help me out

Answer 2

@satellite73

Answer 3

@Jhannybean can you help me please

Answer 4

@dan815 can you help me please

Answer 5

ok

Answer 6

div F integrated in the volume of the closed surface =0

Answer 7

if circulation around any loop is zero then Curl F =0

Answer 8

so is either a or m? @dan815

Answer 9

for a)
u are setting div F =0

Answer 10

everything but a goes to zero when u take the divergence

Answer 11

so a=0

Answer 12

part b) do curl F and and tell me what u get

Answer 13

so you can only determined a?

Answer 14

yes

Answer 15

div F = a

Answer 16

right

Answer 17

and u know that the integral of a over all volume =0 there fore a must be zero

Answer 18

curl f = (7-c)i - (m-10)j + (1-b)k

Answer 19

ok

Answer 20

therefore c=7, m=10,b=1

Answer 21

cool