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Ion beam in E and B field problem

  1. Nov 9, 2009 #1
    1. The problem statement, all variables and given/known data

    A beam of ions enters a region in which the electric field E and magnetic flux density B are normal to each other and both normal to the velocity of the ions. Show that if the velocity of the ions is related to the fields by

    v=ExB/B2

    then the ions pass through the region undeflected.


    2. Relevant equations

    Thinking of using

    F=qvxB

    but not sure.

    3. The attempt at a solution

    Substituting v from info into Lornetz force equation but it doesn't seem to answer the question.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 9, 2009 #2

    lanedance

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    so for the ions to pass through unaffected, the force due to the elctric field & the motion through the magnetic must be equal & opposite (ie exactly cancel)
     
  4. Nov 9, 2009 #3
    So would it be more accurate to use

    qE=qvxB

    and then substitute in the v equation?
     
  5. Nov 9, 2009 #4

    lanedance

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    sounds like a reasonable idea to me, give it a try

    couple of pointers though, just be careful with your signs as the forces neecd to cancel out

    now you could expand a vector triple product or make use of the orthoganalilty of the vectors in teh question & look at the magnitudes...
     
  6. Nov 12, 2009 #5

    gabbagabbahey

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    Gold Member

    If I were you, I would use the general form of the Lorentz force law [itex]\textbf{F}=q(\textbf{E}+\textbf{v}\times\textbf{B})[/itex], and plug in the velocity you are given...after using some vector triple product identities, you should find that the force on each ion [itex]\textbf{F}[/itex] is zero.
     
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