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184_notes:examples:week12_flux_examples [2017/11/08 14:45] – [Solution] tallpaul | 184_notes:examples:week12_flux_examples [2017/11/12 21:11] – [Review of Flux through a Loop] tallpaul | ||
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Suppose you have a magnetic field $\vec{B} = 0.6 \text{ mT } \hat{x}$. Three identical square loops with side lengths $L = 0.5 \text{ m}$ are situated as shown below. The perspective shows a side view of the square loops, so they appear very thin even though they are squares when viewed face on. | Suppose you have a magnetic field $\vec{B} = 0.6 \text{ mT } \hat{x}$. Three identical square loops with side lengths $L = 0.5 \text{ m}$ are situated as shown below. The perspective shows a side view of the square loops, so they appear very thin even though they are squares when viewed face on. | ||
- | {{ 184_notes: | + | {{ 184_notes: |
===Facts=== | ===Facts=== | ||
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* We represent magnetic flux through an area as | * We represent magnetic flux through an area as | ||
$$\Phi_B = \int \vec{B} \bullet \text{d}\vec{A}$$ | $$\Phi_B = \int \vec{B} \bullet \text{d}\vec{A}$$ | ||
- | * We represent the situation with the given representation in the example statement above. | + | * We represent the situation with the given representation in the example statement above. Below, we also show a side and front view of the first loop for clarity. |
+ | {{ 184_notes: | ||
====Solution==== | ====Solution==== | ||
Since the magnetic field has a uniform direction, and the area of the loop is flat (meaning $\text{d}\vec{A}$ does not change direction either), then we can simplify the dot product: | Since the magnetic field has a uniform direction, and the area of the loop is flat (meaning $\text{d}\vec{A}$ does not change direction either), then we can simplify the dot product: |