1. The problem statement, all variables and given/known data Working in Cartesian coordinates (x,y,z) and given that the function g is independent of x, find the functions f and g such that: v=coszi+f(x,y,z)j+g(y,z)k is a Beltrami field. 2. Relevant equations From wolfram alpha a Beltrami field is defined as v x (curl v)=0 3. The attempt at a solution So jumping in, I compute the curl of v and the cross product of the curl of v and v: But then the above nasty equation results and surely this would give rise to some equally nasty PDEs?