Uni Stuff > Mathematics

counter-intuitive divergence

<< < (2/2)

zzdfa:

--- Quote from: /0 on November 27, 2009, 10:46:16 pm ---But does it matter that the arrows get shorter as you go out? It's like if you have a closed gaussian surface, the field lines will be stronger at one side than the other

--- End quote ---

the fact that they do get shorter is what makes this work; have a look at this:
http://en.wikipedia.org/wiki/Inverse_square_law


--- Quote ---. The density of flux lines is inversely proportional to the square of the distance from the source because the surface area of a sphere increases with the square of the radius. Thus the strength of the field is inversely proportional to the square of the distance from the source.
--- End quote ---

/0:
Oh ok, but what if you go back and apply your reasoning to a simple divergence:

-> --> ---> ----> -----> ------> -------->
-> --> ---> ----> -----> ------> -------->
-> --> ---> ----> -----> ------> -------->
-> --> ---> ----> -----> ------> -------->

According to 'gaussian' logic, the divergence should be zero here too

zzdfa:
no. take

->|--> ---> ----> ----->| ------> -------->
->|--> ---> ----> ----->| ------> -------->
->|--> ---> ----> ----->| ------> -------->
->|--> ---> ----> ----->| ------> -------->


clearly there's more going out than there is going in* (area is the same but field strength is different).

/0:
thanks heaps zzdfa, think i've got it now :)

Navigation

[0] Message Index

[*] Previous page