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Calculus and Beyond Homework Help
Vector line integral notation.
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[QUOTE="Craptola, post: 4302708, member: 357233"] One of the example questions I have is. Evaluate [itex]\oint \vec{a}\cdot \vec{dl} [/itex] around the circle [itex]x^{2} +y^{2}=b^{2}[/itex] for [itex]\vec{a}=\frac{\vec{r}}{r^{3}}[/itex]. Where r has its usual meaning is spherical polars. It's nothing complicated I was just never taught what [itex]\vec{dl}[/itex] actually is when represented as a vector, and can't find it anywhere in my notes. My first instinct was to assume that since [itex]\vec{ds}[/itex] is just [itex]ds\mathbf{\hat{n}}[/itex] then [itex]\vec{dl}[/itex] would just be a scalar line element (which in polars I figured would be [itex]rd\phi[/itex]) multiplied by a vector normal to the contour, ie [itex]\mathbf{\hat{r}}[/itex] but after I did the line integral I tried to verify it using stokes theorem only to find that the curl of a is zero. I'm almost certain this is because of the assumption I made on the definition of the vector dl. [/QUOTE]
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Vector line integral notation.
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