# Fundamental Theorem of Line Integration

1. Mar 5, 2013

### Gee Wiz

1. The problem statement, all variables and given/known data
Suppose that F is the inverse square force field below, where c is a constant.
F(r) = c*r/(|r|)^3
r = x i + y j + z k
(a) Find the work done by F in moving an object from a point P1 along a path to a point P2 in terms of the distances d1 and d2 from these points to the origin.

2. Relevant equations

3. The attempt at a solution

Well this is a conservative force because it is dealing with gravity. So i know that the solution is going to be something like F(d2-d1). But how do i write that out? I think that |r| just equals d1 or d2 depending on which one is selected. But how do i get r?

2. Mar 5, 2013

### Gee Wiz

I also thought something like (c*P2)/(d2)^3-(c*P1)/(d1)^3..but thats not right, so i must be missing something

3. Mar 5, 2013

### Dick

Try and guess a potential function that gives you that vector field as a gradient. If you know something about gravity, you might already know the form of the potential function.

4. Mar 5, 2013

### Gee Wiz

So apparently I know nothing about gravity because i can't guess the potential function. I would think that all the vectors would point in towards the more massive object. (in this case towards the origin)

5. Mar 5, 2013

### Dick

Which direction they point depends on the sign of c. Try computing the gradient of 1/|r|. Does it look anything like your vector field?

6. Mar 5, 2013

### Gee Wiz

since r(t)=xi+yj+zk isn't lrl=sqrt(3). That isn't the gradient is it..because del f is like (fx,fy,fz,..etc) ...

7. Mar 5, 2013

### Dick

|r|=sqrt(x^2+y^2+z^2). How is that sqrt(3)?

8. Mar 6, 2013

### Gee Wiz

sorry i meant lr'(t)l