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

bloodhound
in Classical Physics

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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

 

Vx=f(x,y,z)

Vy=g(x,y,z)

Vz=h(x,y,z)

 

how do u find V from those three.

 

cheers

IIRC A common tactic is separatation of variables.

 

Assume Vx = f(x), Vy = f(y), Vz = f(z), such that V=VxVyVz

 

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.

  • Author

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

 

Vx=f(x,z), Vy=g(y,z), and Vz=h(x,y,z)

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