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Line integral of a vector field, F.

The particle (in red) travels from point a to point b along a curve C in a vector field F. Shown below, on the dial at right, is the field's vectors from the perspective of the particle. As it changes orientation, the axis arrows rotate to illustrate the changes in reference. The blue arrow is the field vector relative to the current orientation of the particle.

The dot product of the tangent velocity vector (in red) and the field vector (in blue) results in the value represented as a green bar. This bar "sweeps" an area as the particle travels along the path. This area is equivalent to the line integral.
Source Own work
Author Lucas Vieira
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Other versions Line integral of a scalar field



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25 July 2012


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current 16:00, 9 February 2013 Thumbnail for version as of 16:00, 9 February 2013450 × 410 (316 KB)LucasVBSlower and smoother movement across path (now with constant speed), and more text markers and pauses. Also fixed the uses of "r" instead of "r'"
15:59, 29 July 2012 Thumbnail for version as of 15:59, 29 July 2012450 × 410 (196 KB)LucasVBRemoving hats. Could be confusing.
01:02, 26 July 2012 Thumbnail for version as of 01:02, 26 July 2012450 × 410 (196 KB)LucasVB
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