Non conservative vector fields

In summary, the conversation discusses a vector field, F, with unit vectors, ax, ay, and az, and scalar functions, P, Q, and R. The question asks about the characteristics of P, Q, and R if F is a non-conservative vector field. The response suggests looking at the definition of conservative vector fields and applying it to each component of the vector field.
  • #1
ssrtac
5
0
F(x,y,z)=ax P(x,y,z)+ay Q(x,y,z)+az R(x,y,z)

F is vectoral field. ax , ay and az are unit vectors. P , Q ,R are scalar functions.

The question is this:
If F is non-conservative vectoral field ; what are the characteristics of P Q and R?

thanks in advance. have a nice day
 
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  • #2
This follows from the definition of conservative vector fields in 3-space. Did you check this definition? What exactly are you having trouble with? Look at the definition and see how you can apply each component of the vector field to it.
 

FAQ: Non conservative vector fields

What is a non conservative vector field?

A non conservative vector field is a type of vector field where the line integral of the vector field is dependent on the path taken. In other words, the work done by the vector field on a particle is not only determined by the initial and final positions, but also by the path taken between them.

How is a non conservative vector field different from a conservative vector field?

A conservative vector field is one where the line integral is independent of the path taken. This means that the work done by the vector field only depends on the initial and final positions of the particle. In contrast, a non conservative vector field has a line integral that is path dependent.

What are some examples of non conservative vector fields?

Some examples of non conservative vector fields include force fields with dissipation, such as friction or air resistance, and electromagnetic fields with induced currents. These fields are not conservative because they violate the principle of energy conservation, as energy is lost or gained along different paths.

Can a non conservative vector field have a potential function?

No, a non conservative vector field cannot have a potential function. This is because a potential function is a necessary condition for a vector field to be conservative. If a vector field does not have a potential function, it is not conservative and is therefore non conservative.

Why are non conservative vector fields important in physics?

Non conservative vector fields are important in physics because they allow us to model and understand real-world phenomena that involve energy dissipation or non-conservative forces. These fields play a crucial role in fields such as fluid dynamics, electromagnetism, and thermodynamics, providing a more accurate representation of physical systems.

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