October 17th, 2017, 10:07 PM  #1 
Senior Member Joined: Nov 2015 From: United States of America Posts: 162 Thanks: 21 Math Focus: Calculus and Physics  Work in a force field
Consider a force field $\vec F(x,y)$. If I want to calculate the work done from $(a,b) \rightarrow (c,d)$ on the cartesian plane, and I pick two different paths for my line integral $$\oint_C \vec F \dot \,d\vec s$$ Will I always get the same work for any path taken? I have been messing with a similar problem today and I keep getting different values for work as I try different paths between the same points in the force field. Doesn't seem right 
October 17th, 2017, 11:35 PM  #2  
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,607 Thanks: 819  Quote:
If the force field is conservative, i.e. if it is the gradient of a scalar potential function, then the work done moving a particle through the field between two points will be independent of the path taken. https://en.wikipedia.org/wiki/Conservative_vector_field If the field is not conservative then the work done will vary with the path taken.  
October 17th, 2017, 11:38 PM  #3  
Senior Member Joined: Nov 2015 From: United States of America Posts: 162 Thanks: 21 Math Focus: Calculus and Physics  Quote:
 
October 27th, 2017, 07:12 AM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,829 Thanks: 753 
That's pretty much the definition of "conservative" force field!


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