Finding potential V(x,y,z) of Force field F(x,y,z)

[bloodhound]

Hi ya, I am given a force field F(x,y,z) and i want to find a potential V(x,y,z) such that grad(V)=-F.

 

then I get three

 

partial differential equations

 

V_x=f(x,y,z)

V_y=g(x,y,z)

V_z=h(x,y,z)

 

how do u find V from those three.

 

cheers

[swansont]

IIRC A common tactic is separatation of variables.

 

Assume V_x = f(x), V_y = f(y), V_z = f(z), such that V=V_xV_yV_z

 

Then the solution is fairly straightforward. If you can't separate the variables it's a tougher problem, but many physical solutions behave this way.

[bloodhound]

I dont think i can assume V_x=f(x) etc cos in my problem

 

V_x=f(x,z), V_y=g(y,z), and V_z=h(x,y,z)