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Interesting Magnetism Problem

  1. May 19, 2003 #1
    http://www.geocities.com/bridgestein/Bffield.jpg
    (copy and paste the above address to your browser please)

    In fact I know the answers of this problem, but I have a question.

    Here's the question.
    A charge +q moving with constant velocity v enters into a uniform magnetic field region as shown. The magnetic flux density is B.
    a) What is the direction of the force F experienced by q?
    b) What is the work done by F?
    c) What kind of motion it is performing?
    d) Express the radius of curvature r of the change in terms of B, v, m and q. Where m is the mass of the charge.

    ans:
    a) Direction of force is always perpendicular to the direction of q. The point charge will go upward.

    From the part (d), I know it is performing circular motion and that the work done by F is 0 J!

    d) r = mv/(Bq)

    Why it is performing circular motion? Can't it be an elliptical motion?
     
    Last edited: May 19, 2003
  2. jcsd
  3. May 19, 2003 #2

    Tom Mattson

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    When you have a constant magnitude force that is always perpendicular to the velocity, uniform circular motion is the only possible result. To show this, you can use Newton's second law for the radial component of the force (that is the only nonzero component in this problem):

    ΣFr=qvxB=mar

    where v=vi and B=-Bk. You would then solve the differential equation for the trajectory, using the initial conditions, to see that the path is necessarily circular.
     
  4. May 19, 2003 #3

    Claude Bile

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    Also, if the motion were elliptical, the acceleration would not be perpendicular to the motion and the magnetic field would therefore do work, which is contradictory to your (correct) answer to b).
     
  5. May 20, 2003 #4
    Thanks Tom and Claude Bile
     
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