Note that a potential function is not uniquely defined.

In this case, for every two points
,
we have:

The field
is conservative if, and only if

- 1.
- We have:

Hence, the field is conservative. - 2.
- Let's find a potential for
:
we look for a function
*f*(*x*,*y*,*z*) such that

i.e.

We have:

where*C*_{1},*C*_{2},*C*_{3}are functions of two variables. It follows that:

- 3.
- Take
*A*=(0,0,0) and*B*=(1,2,3). We will compute the integral using two different paths:- (a)
__On the segment__*AB*:A parametrization of the path is:

Thus:

- ;
- .

Now

- (b)
__On a curve:__TakeThus

Now