- #1
nonequilibrium
- 1,439
- 2
Hello. I'm new to vector calculus and I had a question about the following integral:
[tex]\int_{C} x dy[/tex] please note that this is a circulation (I didn't know the tex-code for the little circle sign on the integral)
They calculated this integral (for a specific curve) with the use of a line integral of the tangential component of F (i.e. line integral of a vector field).
But I was wondering, can this be calculated with a line integral of a scalar field? For example if C is the circle with center the origin and radius 1. I suppose for being able to do it with a scalar field, you'd then have to find a parametrization so that ds = x(t) dy(t) right? Is this doable?
(The reason I ask it is not for practical use, but to understand the theory more -- why this can't be done with a scalar field, while it looks so easy)
[tex]\int_{C} x dy[/tex] please note that this is a circulation (I didn't know the tex-code for the little circle sign on the integral)
They calculated this integral (for a specific curve) with the use of a line integral of the tangential component of F (i.e. line integral of a vector field).
But I was wondering, can this be calculated with a line integral of a scalar field? For example if C is the circle with center the origin and radius 1. I suppose for being able to do it with a scalar field, you'd then have to find a parametrization so that ds = x(t) dy(t) right? Is this doable?
(The reason I ask it is not for practical use, but to understand the theory more -- why this can't be done with a scalar field, while it looks so easy)