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Line_integral_of_vector_field.gif (450 × 410 pixels, file size: 316 KB, MIME type: image/gif, looped, 131 frames, 37 s)

Summary

Description

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.
Date
Source Own work
Author Lucas Vieira
Permission
(Reusing this file)
Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.
Other versions Line integral of a scalar field

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depicts

inception

25 July 2012

media type

image/gif

File history

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Date/TimeThumbnailDimensionsUserComment
current16:00, 9 February 2013Thumbnail 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 2012Thumbnail for version as of 15:59, 29 July 2012450 × 410 (196 KB)LucasVBRemoving hats. Could be confusing.
01:02, 26 July 2012Thumbnail for version as of 01:02, 26 July 2012450 × 410 (196 KB)LucasVB

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