What kind of a vector force field is this?

[Keano16]

What kind of a vector force field is this?

Just a general physics question:

I was given a force field vector a(x^2, 2xy, 0) where 'a' is a constant. When I performed a line integral from (0,0,0) to (1,0,0) to (1,1,0), I get 4a/3.

Doing it from (0,0,0) to (0,1,0) to (1,1,0) gives a/3.

From (0,0,0) to (1,1,0) gives a.

As you can see, they are related.


I was wondering what this kind of a force field is known as.. i think someone mentioned something like a "dissipative force field" but I'm not sure. Something along the lines of: if you do some work going in a straight line in one direction, you do the negative of that work when traveling in the opposite direction, giving an overall of 0 work done.


Thanks.

 

[collinsmark]

If a line integral through force field is path independent, it is called a "conservative" force field. If it is path dependent (where you get different answers for different paths, but between the same endpoints), it is not conservative. I suppose I would call it a "non-conservative" force field. But there might be other names too.

 

[dacruick]

non conservative force field is the term I know as well.

 

[Keano16]

I am aware of the concepts of conservative and nonconservative forces, but my tutor said that there is a special name for this case. I remember him distinctly mentioning something along the lines of "dissipative".

 

[collinsmark]

I am aware of the concepts of conservative and nonconservative forces, but my tutor said that there is a special name for this case. I remember him distinctly mentioning something along the lines of "dissipative".

Yeah, that's probably as good of term as any.

You'll encounter these non-conservative ("dissipative," if you'd like) situations when dealing with transformer hysteresis (where the magnetic flux density of the core is not constant, but is dependent upon its previous state), lots of times in thermodynamics (where you have cyclical process, but which involves different sub-processes from getting from point a to b, than it does from getting from point b to a), and numerous other places.

These types of situations invariably describe situations where there is net energy loss, or net energy gain over one cycle of a cyclical system. They're useful in determining the efficiency of a practical power plant, magnetic transformer, heat-pump, etc.