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Two particles and magnetic field

  1. May 6, 2012 #1
    1. The problem statement, all variables and given/known data
    Two particles, 'A' with charge and mass of q and m and 'B' with charge and mass of -q and 2m, each enter at right angles to a uniform magnetic field with the same velocity. Compare the circular paths that each begin upon entering the magnetic field.

    A) A experiences the same force magnitude as that of B and circulates in the same direction as B with A's radius equal to that of B.
    B) B experiences twice force magnitude as that of A and circulates in the opposite direction as A with A's radius at half that of B.
    C) B experiences twice force magnitude as that of A and circulates in the opposite direction as A with A's radius equal to that of B.
    D) A experiences the same force magnitude as that of B and circulates in the opposite direction as B with A's radius at half that of B.



    2. Relevant equations
    Bvq=mv^2/r


    3. The attempt at a solution
    Since the magnetic field is uniform, B can be disregarded. So can v since it is the same velocity for both particles. So the equation can be reduced to q=m/r, and to rearrange and solve for r, r=m/q. Then I plugged in m and q for both particles and I get A=m/q and B=-2m/q. So B circulates the in opposite direction as A, and A has half the radius as B, so that narrows it down to B and D. I'm a little stuck on the force. Does B experience twice the force magnitude as A because B=2m while A=m?
     
  2. jcsd
  3. May 6, 2012 #2
    The gyroradius equation comes straight from the Lorentz force law,

    [tex]\vec{F} = q \vec{v}\times\vec{B}.[/tex]

    So, what can you conclude about the relative forces?
     
  4. May 6, 2012 #3
    They both have the same force magnitude because they both have q for the charge.
     
  5. May 6, 2012 #4
    Exactly. They simply have different motions because they have different masses, and therefore different accelerations when subjected to the same force.
     
  6. May 6, 2012 #5
    Thanks!
     
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