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Induced Voltage in an unclosed loop

  1. Aug 21, 2015 #1
    I read the following problem on a text book:

    A airplane flies at a constant speed of 680m/s perpendiculary to earth's magnetic field (of 5x10^-5 T). The wingspan of the airplane is 9.8m. What is the induced voltage?
    The answer the book gives is: E = BLv = 0.4066V

    But I've been wondering if this is true. There isn't and enclosed loop. How can a simple wire moving on a magnetic field induce voltage on its terminals?

    http://www.physics.sjsu.edu/becker/physics51/30_25_Lenz%27s_law_(Exercise_30-16).JPG
     

    Attached Files:

  2. jcsd
  3. Aug 21, 2015 #2

    Henryk

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    Gold Member

    Actually, when I plugged the numbers, I got 0.3332 V. But yes, there is a voltage induced across the wings. If the wingtips were touching two parallel and stationary rails, you could measure the voltage between the rails ( or power a light bulb)
     
  4. Aug 24, 2015 #3
    Apart from the numbers, the physical result is quite correct. You don't have to close the loop to get a voltage. Because of the velocity of the airplane, electrons in the wings have a magnetic force acting on them, pushing them toward the point a in your picture. This results in accumulation of electrons near point a, leaving behind an equal positive charge near point b. This separation of charges results in a voltage, with b at a higher, and a at a lower voltage. So this phenomenon is due to a magnetic force, and not due to induction.
     
  5. Aug 24, 2015 #4
    Try understanding the reason for the induced voltage - when the rod moves through a magnetic field, a force acts on the electrons of the rod. This pushes them towards one side , developing an area containing excess of electrons, and at the same time a deficiency of them on the other.

    This leads to an electric field, and consequently, a potential difference across the rod. Understand, if it was a closed loop, provided it was conducting, there would be , simply, a current flowing through the loop.

    Hope this helps.
     
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