Finding force vector fields for 3 dimensional potential energy fields

AI Thread Summary
To find the force vector fields for the specified 3-dimensional potential energy fields, the relationship between force and potential energy is defined by the equation F(x,y,z) = -∇V(x,y,z). The potential energy functions provided include terms with constants a, α, β, ɣ, b, σ, ϑ, and ρ, which require unit analysis to determine their dimensions in SI units. The discussion highlights the challenge of understanding how to derive force fields from potential energy and the need for clarity on the treatment of constants involved. Participants express difficulty in locating relevant resources or guidance in textbooks or online. Understanding the relationship between potential energy and force is crucial for solving these types of problems.
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Homework Statement


Find the force vector fields (in terms of x, y, z, and any constants) for each of the following 3-dimensional potential energy fields

Question B:
Assume SI units for force, energy, and lengths x, y, z: What must be the units of each of the constants?

Homework Equations


a) V(x,y,z) = a(xyz) + C
b) V(x,y,z) = αx² + βy² + ɣz² + D
c) V(x,y,z) = b e –( σx +ϑy + ρz)

The Attempt at a Solution


I honestly don't even know where to begin with this. I can't find anything about it in my book, nor does google give me any tips. Could someone describe how to treat such a question?
 
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\vec{F}(x,y,z)=-\vec{\nabla}V(x,y,z)
 

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