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Magnetic force help

  1. May 26, 2008 #1
    1. The problem statement, all variables and given/known data
    An electron moves in a circular path in a vacuum under the influence of a magnetic field perpendicular to and into the paper.If there is another electron which moves with a higher speed in a circular path in the same B-field, state and explain how each of the following will be affected as compared to the first electron?
    (c) The radius of the circular path

    2. Relevant equations
    F = Bqv
    B = flux density
    q = charge
    v = velocity of the charge

    3. The attempt at a solution

    F(m) = Bqv
    Since F(m) causes the centripetal acceleration of electron
    F(m) = Bqv = mv^2/r
    r = mv/Bq
    Therefore it can be concluded that r increases as v increases?

    But how can this be case as,
    F(m) = Bqv, and F(m) increases as velocity of the charge increases
    If F(m) increases, r would decrease as it is inversely proportional to F
    in the equation F(m) = mv^2/r.

    So would r increase or decrease if a faster electron moves in a circular path in a vacum under the influence of a magnetic field perpendicular to and into the paper.

    Attached Files:

  2. jcsd
  3. May 26, 2008 #2


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    Staff Emeritus
    Science Advisor
    Gold Member

    You have clearly put a lot of thought into this question, perhaps a little too much :wink:. Consider your final equation,

    [tex]F = \frac{mv^2}{r}[/tex]

    And your final comment,
    You are correct that the magnetic force increases, but you forget that the speed v has also increased. Notice that the speed is raised to the second power and therefore will have a much greater effect on the magnetic force that the radius since the radius is only raised to the fist power.
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