Question

Prove that for a conversation field F cruel F =0

Answer 1

Answer:

thanks for free point ..

Answer 2

Answer:

I found an algorithm that seems to work out, but perhaps someone can advise me where the divergence free comes into-play to power this algorithm.

Let F be a Euclidean vector-field such that ∇⋅F=0. If there exists a vector-field A such that F=∇×A, then we have the following set of equations. Additionally, I have found that they have the corresponding solutions, where ⊕ is the exclusive or symbol:

∂Az∂y−∂Ay∂z=Fx:Az=∫Fxdy⊕Ay=−∫Fxdz

−(∂Az∂x−∂Ax∂z)=Fy:Az=−∫Fydx⊕Ax=∫Fydz

∂Ay∂x−∂Ax∂y=Fz:Ay=∫Fzdx⊕Ax=−∫Fzdy

These exclusive or ⊕ solutions yield two choices for A