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Force of a wire induced by earth magnetic field

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  1. Mar 1, 2016 #1
    1. The problem statement, all variables and given/known data
    The power cable for an electric trolley (see figure) carries a horizontal current of 330 A toward the east. The Earth's magnetic field has a strength 5.0 ✕ 10-5 T and makes an angle of dip of24° at this location. Calculate the magnitude and direction of the magnetic force on a 20 m length of this cable.
    27-p-075.gif
    2. Relevant equations

    F=BILsinΘ

    3. The attempt at a solution

    I thought the question means there B and I form a 24° angle, so I tried F= 5.0 x 10^-5 x 20 x 330 x sin 24°. However, it seems that the answer is F=BILsin90, and the direction of the magnetic force is 66 above the horizontal towards the north. How can a magnetic force not perpendicular to the plane of B and I? I am really confused. Please help me here, thanks!
     
  2. jcsd
  3. Mar 1, 2016 #2

    TSny

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    Hello.

    Note that the current is toward the east.

    How is this direction related to the direction of B?
     
    Last edited: Mar 1, 2016
  4. Mar 1, 2016 #3
    Thanks for your reply!

    This is where I got confused.
    So the current is toward east, and the direction of B is towards the northeast, and the angle is 24. So B and I form a angle of 66. - That's how I interpret the angle of dip. Is this wrong?
     
  5. Mar 1, 2016 #4

    TSny

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    The B field is not northeast. The B field has a vertically downward component and a horizontal component (parallel to the ground). The horizontal component is toward the north. Looking at the picture, you are facing north as the current flows east. The B field has a horizontal component into the picture and also a vertical component from the top of the picture toward the bottom of the picture.
     
  6. Mar 1, 2016 #5
    Got it! Thank you so much.
     
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