184_notes:examples:week12_changing_shape

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184_notes:examples:week12_changing_shape [2018/04/11 19:39] – [Solution] pwirving184_notes:examples:week12_changing_shape [2018/08/09 18:08] (current) – curdemma
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 +[[184_notes:b_flux|Return to Changing Magnetic Flux notes]]
 +
 ===== Flux Through a Changing, Rotating Shape ===== ===== Flux Through a Changing, Rotating Shape =====
 Suppose you have a magnetic field directed in the $-\hat{z}$-direction, into the page. There is a flexible, circular loop situated on the page, in the $xy$-plane. You stretch it out in the $\pm x$-direction like a rubber band to change its area. Then you rotate it $90^\text{o}$ in the $xy$-plane. Finally, you rotate the loop $60^\text{o}$ in the $yz$-plane. What happens to the magnetic flux through the loop during these steps? Suppose you have a magnetic field directed in the $-\hat{z}$-direction, into the page. There is a flexible, circular loop situated on the page, in the $xy$-plane. You stretch it out in the $\pm x$-direction like a rubber band to change its area. Then you rotate it $90^\text{o}$ in the $xy$-plane. Finally, you rotate the loop $60^\text{o}$ in the $yz$-plane. What happens to the magnetic flux through the loop during these steps?
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   * We represent the steps with the following visual:   * We represent the steps with the following visual:
  
-{{ 184_notes:12_steps_for_loop.png?1000 |Steps}}+[{{ 184_notes:12_steps_for_loop.png?1000 |Steps}}]
 ====Solution==== ====Solution====
 Since the magnetic field has a uniform direction, and the area of the loop is flat (meaning $d\vec{A}$ does not change direction if we move along the area), then we can simplify the dot product: Since the magnetic field has a uniform direction, and the area of the loop is flat (meaning $d\vec{A}$ does not change direction if we move along the area), then we can simplify the dot product:
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  • Last modified: 2018/04/11 19:39
  • by pwirving