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| 184_notes:examples:week12_flux_examples [2017/11/08 15:12] – [Review of Flux through a Loop] tallpaul | 184_notes:examples:week12_flux_examples [2018/08/09 18:08] (current) – curdemma | ||
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| ===== Review of Flux through a Loop ===== | ===== Review of Flux through a Loop ===== | ||
| 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: | ||