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Magnetic Field Problem

  1. Sep 1, 2007 #1
    1. The problem statement, all variables and given/known data
    What are the magnetic field strength and direction at the dot in Figure Ex32.8, in which v = 3.0*10^7 m/s?

    Figure Ex.32.8 is attached to the this post.
    r = 0.02828 m
    m0/4pi = 10^-7 T
    v = 3.0*10^7 m/s
    q = 1.60217653*10^-19 C

    2. Relevant equations
    Biot-Savart Law (attached), can't really type it...


    3. The attempt at a solution

    Ok. It's probably a very simple problem and it makes me feel really bad 'cause I can't solve it... I've tried to solve it with the Biot-Savart Law (check attach) with the values I mentioned above

    I'm sure I calculated the cross product wrong.. How would I calculate it in this case? Thanks in advance.
     

    Attached Files:

  2. jcsd
  3. Sep 1, 2007 #2

    Astronuc

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    Staff: Mentor

    Try writing the vector v and [itex]\hat{r}[/itex] in the [itex]\hat{x}, \hat{y}[/itex] form, and then write the cross product.
     
  4. Sep 1, 2007 #3
    First, thanks for replying to my post. Second, here's what I did:
    vector v = 0i + 3.0*10^7j
    [itex]\hat{r}[/itex]=-0.01/0.028i - 0.01/0.028j
    Now, hopefully, that's correct. With that, the only thing left to do is multiply
    m0/4pi * q/r, which is 2.003*10^-23 by [itex]\hat{r}[/itex] and then cross
    it with vector v, right?
     
  5. Sep 1, 2007 #4

    learningphysics

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    Homework Helper

    Your r vector is just -0.02i -0.02j. Other than that everything looks good.
     
  6. Sep 1, 2007 #5

    Doc Al

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    Staff: Mentor

    That unit vector should be (approximately): [itex]\hat{r}[/itex]=-0.02/0.028i - 0.02/0.028j
    (Which is consistent with what learningphysics said about the vector r.)
     
  7. Sep 1, 2007 #6

    learningphysics

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    Ah yes... I apologize. you need the unit vector in the r direction, not the r vector itself.
     
  8. Sep 1, 2007 #7
    And when I'm crossing the two, I'll just need to multiply v by r and then by sin 45, right?
     
  9. Sep 1, 2007 #8

    learningphysics

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    Homework Helper

    You're crossing v with the unit vector in the r direction... hence it's just v*1*sin45, that gives the magnitude of the cross product.

    so the magnitude of [tex]\hat{r}[/tex] x [tex]\vec{v}[/tex] is just vsin45, where [tex]\hat{r}[/tex] is a unit vector in the r direction.
     
    Last edited: Sep 1, 2007
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