184_notes:examples:week12_decreasing_flux

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184_notes:examples:week12_decreasing_flux [2017/11/12 18:32] – dmcpadden184_notes:examples:week12_decreasing_flux [2018/08/09 18:46] (current) – curdemma
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 +[[184_notes:ind_i|Return to The Curly Electric Field and Induced Current notes]]
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 ===== Decreasing Flux ===== ===== Decreasing Flux =====
 Say we have a bar that is sliding down a pair of connected conductive rails (so current is free to flow through the loop created by the bar and rails), which is sitting in a magnetic field that points into the page. If the bar slides along the rails to decrease the area of the loop, what happens? Say we have a bar that is sliding down a pair of connected conductive rails (so current is free to flow through the loop created by the bar and rails), which is sitting in a magnetic field that points into the page. If the bar slides along the rails to decrease the area of the loop, what happens?
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   * We represent the steps with the following visual:   * We represent the steps with the following visual:
  
-{{ 184_notes:12_rail_flux.png?400 |Flux Through Loop}}+[{{ 184_notes:12_rail_flux.png?400 |Flux Through Loop}}]
 ====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 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 $\text{d}\vec{A}$ does not change direction if we move along the area), then we can simplify the dot product:
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 It will be easier to concern ourselves with this value, rather than try to describe the integral calculation each time. As the bar begins moving to the left, the area within the loop begins to close up, as shown below: It will be easier to concern ourselves with this value, rather than try to describe the integral calculation each time. As the bar begins moving to the left, the area within the loop begins to close up, as shown below:
  
-{{ 184_notes:12_rail_flux_decreased.png?400 |Decreased Flux}}+[{{ 184_notes:12_rail_flux_decreased.png?400 |Decreased Flux}}]
  
 It should be easy to see the that the magnetic field and the orientation of the loop are not changing, but the area of the loop is decreasing. **The flux through the loop is therefore decreasing, which indicates that a current is induced in the loop**. It should be easy to see the that the magnetic field and the orientation of the loop are not changing, but the area of the loop is decreasing. **The flux through the loop is therefore decreasing, which indicates that a current is induced in the loop**.
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 Alternatively, you could think of the mobile charges inside the moving bar. Since the bar is moving inside a magnetic field, mobile charges will experience an acceleration due to the magnetic force. The force is $\vec{F} = q \vec{v} \times \vec{B}$, which points down for positive charges, implying that conventional current will be clockwise, which is the same result we reached using Faraday's law. The result is shown below. Alternatively, you could think of the mobile charges inside the moving bar. Since the bar is moving inside a magnetic field, mobile charges will experience an acceleration due to the magnetic force. The force is $\vec{F} = q \vec{v} \times \vec{B}$, which points down for positive charges, implying that conventional current will be clockwise, which is the same result we reached using Faraday's law. The result is shown below.
  
-{{ 184_notes:12_rail_current.png?300 |Induced Current}}+[{{ 184_notes:12_rail_current.png?300 |Induced Current}}] 
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 +{{youtube>lGpZ63wuroY?large}}
  • 184_notes/examples/week12_decreasing_flux.1510511566.txt.gz
  • Last modified: 2017/11/12 18:32
  • by dmcpadden