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A rather tricky magnetic field problem.

  1. Mar 17, 2008 #1
    1. The problem statement, all variables and given/known data
    A proton moves through a region of space where there is a magnetic field [tex]\vec{B}[/tex]= (0.61[tex]\hat{i}[/tex] + 0.36[tex]\hat{j}[/tex]) T and an electric field
    [tex]\vec{E}[/tex]= (2.8[tex]\hat{i}[/tex] - 4.3[tex]\hat{j}[/tex]) *10[tex]^{3}[/tex] V/m. At a given instant, the proton's velocity is [tex]\vec{v}[/tex]= (6.3[tex]\hat{i}[/tex] + 2.9[tex]\hat{j}[/tex] - 4.8[tex]\hat{k}[/tex]) *10[tex]^{3}[/tex] m/s.

    Determine the components of the total force on the proton.
    F[tex]_{x}[/tex]= ?, F[tex]_{y}[/tex]= ?, F[tex]_{z}[/tex]=?

    2. Relevant equations
    I assume what needs to be used is the "Lorentz Equation" which is:
    [tex]\vec{F}[/tex]= q([tex]\vec{E}[/tex] + [tex]\vec{V}[/tex] * [tex]\vec{B}[/tex])
    and use the q of a proton which is 1.6*10[tex]^{-19}[/tex].

    3. The attempt at a solution
    I attempted to use a cross product of [tex]\vec{V}[/tex] and [tex]\vec{B}[/tex] and it seemed to be on the right track but I ended up getting stuck on what to do with [tex]\vec{E}[/tex] and honestly I ended up getting stuck on the whole problem and not sure at this point where to start and end.
  2. jcsd
  3. Mar 17, 2008 #2


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    Gold Member

    Your on the right track.

    HINT: Try starting by working out the cross product and getting it in terms of components. Then, group all the x component terms together, all the y component terms together, etc. (This includes the E field terms as well.) Do you see how you can get your answer from here on out?
  4. Mar 17, 2008 #3
    How'd you get stuck on E? V cross B times the scalar q gives you a vector, and q*E is a vector. Do you remember how to add two vectors?

    Then you'll have the force vector, with its x, y, and z components
  5. Mar 17, 2008 #4
    I would say I am a bit rusty when it comes to vectors, I did attempt to do the basic vector addition and the answer I imputed the online homework application disliked lol.
  6. Mar 17, 2008 #5
    I got the answers


    and the homework program told me to check my signs, and told me I was incorrect. What did I do wrong?
  7. Mar 17, 2008 #6
    I keep trying to do the cross product, then adding the vectors together and the third vector never seems to work out right.
  8. Mar 17, 2008 #7
    I havent been doing vectors much, but isnt it just possible to take each composant at a time? So for example Fi=Ei*Q + Q*Vk*Bj. Then no vector addition is required.
  9. Mar 17, 2008 #8
    Out of curiousity, what then would be the setup for Fj and Fk?
  10. Mar 17, 2008 #9


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    What do you get when you work out v X B?
  11. Mar 18, 2008 #10
    If my theory is correct, it should be like:

    it seems like the the +/- depends on how you define the positive directions for y/x/z in k/i/j, so im not sure on these.
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