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184_notes:b_flux [2021/04/08 14:22] – dmcpadden | 184_notes:b_flux [2021/06/17 15:28] – [Magnetic Flux] bartonmo | ||
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In these notes, we will start thinking the right hand side of Faraday' | In these notes, we will start thinking the right hand side of Faraday' | ||
- | In general, any sort of **flux** is how much of something goes through an area. For example, we could think of a child' | + | In general, any sort of **flux is how much of something goes through an area**. For example, we could think of a child' |
- | **Magnetic | + | Therefore |
/* | /* | ||
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$$\Phi_{B}= \vec{B} \bullet \vec{A}$$ | $$\Phi_{B}= \vec{B} \bullet \vec{A}$$ | ||
- | [{{184_notes: | + | [{{184_notes: |
where $\Phi_{B}$ is the magnetic flux (with units of $T \cdot m^2$), $\vec{B}$ is the magnetic field and $\vec{A}$ is the area vector. **The area vector in this case is the vector that has the same magnitude as the area (i.e. length times width for a rectangular area or $\pi r^2$ for a circular area) and has a direction that is perpendicular to the area**, which is represented by the green arrow in the figure to the right. (This is exactly the same as with electric flux). You may notice that there are actually two different vectors that are perpendicular to the gray surface. We've drawn the green arrow in the $+y$ direction, but we could have also picked the vector that points in the $-y$ direction. For an open surface, it doesn' | where $\Phi_{B}$ is the magnetic flux (with units of $T \cdot m^2$), $\vec{B}$ is the magnetic field and $\vec{A}$ is the area vector. **The area vector in this case is the vector that has the same magnitude as the area (i.e. length times width for a rectangular area or $\pi r^2$ for a circular area) and has a direction that is perpendicular to the area**, which is represented by the green arrow in the figure to the right. (This is exactly the same as with electric flux). You may notice that there are actually two different vectors that are perpendicular to the gray surface. We've drawn the green arrow in the $+y$ direction, but we could have also picked the vector that points in the $-y$ direction. For an open surface, it doesn' | ||
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where $\theta$ is the angle between the magnetic field and the area vector. This should also make some physical sense. As shown in the top figure to the left, if the magnetic field (shown in blue arrows) and area vector (red arrow) point in the same direction, then the dot product turns into a simple multiplication and $cos(\theta)=1$. If we look at the figure, there are lots of magnetic field arrows poking through the surface, so we'd expect a large magnetic flux. As shown in the bottom figure to the left, if the magnetic field (blue arrows) points perpendicular to the area vector (green arrow), then the dot product gives a zero since $cos(90) = 0$. If we look at the figure, we see this result as well because none of the magnetic field arrows actually go through the surface. | where $\theta$ is the angle between the magnetic field and the area vector. This should also make some physical sense. As shown in the top figure to the left, if the magnetic field (shown in blue arrows) and area vector (red arrow) point in the same direction, then the dot product turns into a simple multiplication and $cos(\theta)=1$. If we look at the figure, there are lots of magnetic field arrows poking through the surface, so we'd expect a large magnetic flux. As shown in the bottom figure to the left, if the magnetic field (blue arrows) points perpendicular to the area vector (green arrow), then the dot product gives a zero since $cos(90) = 0$. If we look at the figure, we see this result as well because none of the magnetic field arrows actually go through the surface. | ||
- | [{{184_notes: | + | [{{184_notes: |
(As a side note, this technically gives you the magnitude of the flux. Flux can be positive or negative and that depends on how the area vector points relative to the magnetic field vectors. This is discussed further in the [[184_notes: | (As a side note, this technically gives you the magnitude of the flux. Flux can be positive or negative and that depends on how the area vector points relative to the magnetic field vectors. This is discussed further in the [[184_notes: |