basic_tools:vector_calculus:curl
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basic_tools:vector_calculus:curl [2017/12/16 14:16] jakobadmin created |
basic_tools:vector_calculus:curl [2018/03/28 12:25] (current) jakobadmin |
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| ====== Curl ====== | ====== Curl ====== | ||
| - | <tabbox Why is it interesting?> | ||
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| - | The curl of a quantity: $\Delta \times F$ is a crucial tool that allows us how much a given system "rotates". For example, when we try to describe water, the curl of the quantity that we use to describe the water, tells us how much rotation is going on in the water. | ||
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| - | The curl is especially important in electrodynamics, because the fundamental equations of electrodynamics (called [[equations:maxwell_equations|Maxwell equations]]) contain the curl of the electric and magnetic fields. | ||
| - | <tabbox Layman> | + | <tabbox Intuitive> |
| <blockquote>Circulation is the amount of force that pushes along a closed boundary or path. It's the total "push" you get when going along a path, such as a circle. | <blockquote>Circulation is the amount of force that pushes along a closed boundary or path. It's the total "push" you get when going along a path, such as a circle. | ||
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| A vector field is usually the source of the circulation. If you had a paper boat in a whirlpool, the circulation would be the amount of force that pushed it along as it went in a circle. The more circulation, the more pushing force you have. | A vector field is usually the source of the circulation. If you had a paper boat in a whirlpool, the circulation would be the amount of force that pushed it along as it went in a circle. The more circulation, the more pushing force you have. | ||
| - | Curl is simply the circulation per unit area, circulation density, or rate of rotation (amount of twisting at a single point). Imagine shrinking your whirlpool down smaller and smaller while keeping the force the same: you'll have a lot of power in a small area, so will have a large curl. If you widen the whirlpool while keeping the force the same as before, then you'll have a smaller curl. And of course, zero circulation means zero curl.<cite>[[https://betterexplained.com/articles/vector-calculus-understanding-circulation-and-curl/|Vector Calculus: Understanding Circulation and Curl]] by Kalid Azad</cite></blockquote> | + | **Curl is simply the circulation per unit area, circulation density, or rate of rotation (amount of twisting at a single point)**. Imagine shrinking your whirlpool down smaller and smaller while keeping the force the same: you'll have a lot of power in a small area, so will have a large curl. If you widen the whirlpool while keeping the force the same as before, then you'll have a smaller curl. And of course, zero circulation means zero curl.<cite>[[https://betterexplained.com/articles/vector-calculus-understanding-circulation-and-curl/|Vector Calculus: Understanding Circulation and Curl]] by Kalid Azad</cite></blockquote> |
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| - | <tabbox Student> | + | <tabbox Concrete> |
| * [[https://betterexplained.com/articles/vector-calculus-understanding-circulation-and-curl/|Vector Calculus: Understanding Circulation and Curl]] by Kalid Azad | * [[https://betterexplained.com/articles/vector-calculus-understanding-circulation-and-curl/|Vector Calculus: Understanding Circulation and Curl]] by Kalid Azad | ||
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| - | <tabbox Researcher> | + | <tabbox Abstract> |
| <note tip> | <note tip> | ||
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| - | <tabbox Examples> | + | <tabbox Why is it interesting?> |
| - | --> Example1# | + | The curl of a quantity: $\nabla \times F$ is a crucial tool that allows us how much a given system "rotates". For example, when we try to describe water, the curl of the quantity that we use to describe the water, tells us how much rotation is going on in the water. |
| - | + | The curl is especially important in [[models:classical_electrodynamics|electrodynamics]], because the fundamental equations of electrodynamics (called [[equations:maxwell_equations|Maxwell equations]]) contain the curl of the electric and magnetic fields. | |
| - | <-- | + | |
| - | --> Example2:# | ||
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| - | <-- | ||
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| - | <tabbox FAQ> | ||
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| - | <tabbox History> | ||
| </tabbox> | </tabbox> | ||
basic_tools/vector_calculus/curl.1513430182.txt.gz · Last modified: 2017/12/16 13:16 (external edit)
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