MHB Multivariable conservative field

[kenporock]

Goodnight,

How can I find a conservative field F, such that ∫F ds = 0 without C being a closed path
Can i have some examples ?

 

[I like Serena]

Goodnight,

How can I find a conservative field F, such that ∫F ds = 0 without C being a closed path
Can i have some examples ?

Hi kenporock, welcome to MHB! (Wave)

Consider the force of gravity.
Now move an object around, such that it ends up on the same height it had at the beginning.
The work done by gravity $∫\mathbf F\cdot d\mathbf s$ is then zero.
That is, the object has the same potential energy again.