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Divergence_Curl_in_a_nutshell

Divergence_Curl_in_a_nutshell - vector field that is...

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Divergence and Curl in a nutshell As an undergraduate student, I found Divergence and Curl operators to be quite confusing. That is why I am providing this graphical presentation to you. to you. Hope this helps. Divergence: Divergence measures the rate at which a vector field changes along the direction of the vector at a particular point. If the vector field keeps increasing as one moves along the direction of the vector, it has a positive divergence. If it decreases along its direction then divergence is negative. Example: Positive divergence: Negative divergence: Curl: Curl measures how a vector field changes perpendicular to its direction. However, there are two mutually perpendicular directions (arbitrarily chosen) to a vector. Hence for a
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Unformatted text preview: vector field that is directed along the x-axis, its curl can have nonzero components along y or z directions. Example: This vector field has a curl along the negative-z axis. In other words, the z-component of the curl for this vector field measures how the above vector field changes in the y-direction. As an another example, consider the velocity field in a river, that would something like the following: This vector field will have an upward curl near the upper bank ( U ) of the river and a downward curl near the bottom bank ( B ). Imagine the shape of the vector field which is curl of the above field. y x B U...
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