Automoderated users, edit
3,552
edits
Changes
→Definition
===Two Dimensions===
===Two Dimensions===
The obvious form of this for a two-dimensional vector field would be the limit of a line integral on a circle around a point, with one minor exception: usually, when we take the line integral of a vector field, we examine the dot product of the field with the curve tangent. However, in this case, we will examine the dot product of the field with the outward pointing curve normal, which for a circle, is <math>-\partial_s \vec{T}</math> where the derivative is taken with regard to arc length on the circle ''s''.
Therefore, in two dimensions, we have:
<math>\operatorname{div}\ \vec{F} = \lim_{r\to 0} \left( \frac{1}{\pi r^2} \oint_C \vec{F}\cdot\frac{-d\vec{T}}{ds} dA \right)</math>
==Computation==
==Computation==