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Magnetic Field Force

  1. Mar 28, 2016 #1
    1. The problem statement, all variables and given/known data
    A proton moves through a uniform magnetic field given by Barrowitalic.gif = (10 ihat.gif −25.3(j-hat) + 30(k-hat))mT. At time t1, the proton has a velocity given by varrowitalic.gif = vx ihat.gif + vy(j-hat)+ (2.0 km/s)(k-hat) and the magnetic force on the proton is Farrowitalic.gif B = (4.46 ✕ 10−17 N) ihat.gif + (1.76 ✕ 10−17 N)(j-hat).

    At this instant, what is Vx?

    2. Relevant equations
    F= qV x B

    3. The attempt at a solution
    F/qB= V (using all the i-hat values since Im looking for Vx)
    (4.46x10^-17)/(1.6x10^-19)(0.001)
    This gives me= 278750 m/s
     
  2. jcsd
  3. Mar 28, 2016 #2

    gneill

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    Staff: Mentor

    Your relevant equation involves a cross product, so each force component will involve a mix of contributions from other components of the velocity and field vectors.

    I suggest that you expand the cross product in the equation symbolically first, then pick out useful equations from the force terms.
     
  4. Mar 28, 2016 #3
    ok I have expanded the cross product and got this;

    (Vy)(30) - (2000)(-25.6) = 30Vy + 512000
    (2000)(10) - (Vx)(30) = 20,000 - 30Vx
    (Vx)(-25.6) - (Vy)(-25.6) = -25.6Vx + 25.6Vy

    So the relevant equation would be the second, since it has a Vx. I set that equal to 1.76E-17/ e and solved for Vx which did not work.
     
  5. Mar 28, 2016 #4

    gneill

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    Staff: Mentor

    I don't see where you've accounted for the charge on the proton or the given units of the magnetic field terms (milli Teslas).
     
  6. Mar 28, 2016 #5
    I accounted for the charge by dividing by e, and just redid the calculation with 0.03 instead of 30.
     
  7. Mar 28, 2016 #6

    gneill

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    Staff: Mentor

    That accounts for the ##B\hat{k}## term. What about the ##B\hat{i}## term (10 mT)?
     
  8. Mar 28, 2016 #7
    Thank you so much!!! that cleared it up!!
     
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