Question

"The divergence of a field at a point is actually defined as the limit of the flux of a vector field through a surface as the size of the surface shrinks to zero. "



http://prntscr.com/99rnji

Lets try and prove the divergence to flux relation by working out what it says in the blue text in that attached screenshot

Answer 1

@inkyvoyd

Answer 2

Do you want definition of flux?

Answer 3

ye :)

Answer 4

okay cool lets work on it hehe

Answer 5

okay :D

Answer 6

okay got that

Answer 7

so Flux of a surface is defined as the sum of the magnitude of the vector field that is perpendicular to that surface.

Answer 8

yes

Answer 9

okay So now lets work on it

Answer 10

but what does the ques mean?
divergence of flux?

Answer 11

Sorry, what do you not understand now?

Answer 12

we gotta do this->prove the divergence to flux relation by working out what it says in the blue text in that attached screenshot.
In this question what is the meaning of divergence of flux?

Answer 13

does it mean rate of flux expansion or something?

Answer 14

http://prntscr.com/99rxy1

Answer 15

\[F_x(x+dx,y,z)-F_x(x,y,z)\]
is the flux out, also if you prove this you have basically proved Gauss' theorem!