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184_notes:examples:week12_flux_examples [2017/11/08 14:45] – [Solution] tallpaul | 184_notes:examples:week12_flux_examples [2018/08/09 18:08] (current) – curdemma |
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| [[184_notes:b_flux|Return to Changing Magnetic Flux notes]] |
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===== Review of Flux through a Loop ===== | ===== Review of Flux through a Loop ===== |
Suppose you have a magnetic field →B=0.6 mT ˆx           . Three identical square loops with side lengths L=0.5 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 →B=0.6 mT ˆx           . Three identical square loops with side lengths L=0.5 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. |
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{{ 184_notes:12_three_loops.png?400 |Square Loops in the B-field}} | [{{ 184_notes:12_three_loops.png?600 |Square Loops in the B-field}}] |
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===Facts=== | ===Facts=== |
* We represent magnetic flux through an area as | * We represent magnetic flux through an area as |
ΦB=∫→B∙d→A | ΦB=∫→B∙d→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. |
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| [{{ 184_notes:12_first_loop.png?500 |First Loop}}] |
====Solution==== | ====Solution==== |
Since the magnetic field has a uniform direction, and the area of the loop is flat (meaning d→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 d→A  does not change direction either), then we can simplify the dot product: |