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| 184_notes:what_happens [2021/04/08 13:55] – dmcpadden | 184_notes:what_happens [2021/04/08 13:56] – dmcpadden |
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| Mathematically, we represent this relationship using [[https://en.wikipedia.org/wiki/Curl_(mathematics)|a vector operation called curl]]; however, for this class, we will generally simplify the curl operation (using [[https://en.wikipedia.org/wiki/Stokes%27_theorem|Stokes' Theorem]]) to be: | Mathematically, we represent this relationship using [[https://en.wikipedia.org/wiki/Curl_(mathematics)|a vector operation called curl]]; however, for this class, we will generally simplify the curl operation (using [[https://en.wikipedia.org/wiki/Stokes%27_theorem|Stokes' Theorem]]) to be: |
| $$\int \vec{E}_{nc} \bullet d\vec{l} = - \frac{d\Phi_{B}}{dt}$$ | $$\int \vec{E}_{nc} \bullet d\vec{l} = - \frac{d\Phi_{B}}{dt}$$ |
| Where this equation (called [[https://en.wikipedia.org/wiki/Faraday%27s_law_of_induction|Faraday's Law]]) says that the curly electric field ($$ \vec{E}_{nc}$$) around a loop ($$d\vec{l}$$) is equal to the //opposite// change in the magnetic flux ($$\frac{d\Phi_{B}}{dt}$$) through that loop. The next few pages of notes will go through each part of this equation in detail (including where the negative sign came from) and how to use it, but it's important to remember that the relationship behind this equation is that a changing magnetic field will create a curly electric field. | Where this equation (called [[https://en.wikipedia.org/wiki/Faraday%27s_law_of_induction|Faraday's Law]]) says that the curly electric field ($ \vec{E}_{nc}$) around a loop ($d\vec{l}$) is equal to the //opposite// change in the magnetic flux ($\frac{d\Phi_{B}}{dt}$) through that loop. The next few pages of notes will go through each part of this equation in detail (including where the negative sign came from) and how to use it, but it's important to remember that the relationship behind this equation is that a changing magnetic field will create a curly electric field. |
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| ==== Examples ==== | ==== Examples ==== |
| Video example showing a constant flux, rotating loop, and the magnetic being pushed towards and away from the loop: | Video example showing a constant flux, rotating loop, and the magnetic being pushed towards and away from the loop: |
| {{youtube>mMh9pyxa0o8?large}} | {{youtube>mMh9pyxa0o8?large}} |