- #1
broegger
- 257
- 0
Suppose we have a conservative vector field on a plane. Suppose also that we have a closed curve C on that plane. Then we have:
[tex] \int_C \mathbf{F}\cdot d\mathbf{r} = 0 [/tex]
The line integral around C is zero because F is conservative. Here is what I don't understand:
If you have one or more singularities (points at which F is undefined) within the area bound by C then the line integral around C is no longer zero! How can this be?
[tex] \int_C \mathbf{F}\cdot d\mathbf{r} = 0 [/tex]
The line integral around C is zero because F is conservative. Here is what I don't understand:
If you have one or more singularities (points at which F is undefined) within the area bound by C then the line integral around C is no longer zero! How can this be?