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Homework Help: Electric Charge in a Magnetic Field

  1. Apr 1, 2005 #1
    1) For a particle of mass m and a charge of q moving in a circular path in a magnetic field B, show that its kinetic energy is proportional to r^2, the square of the radius of the curvature of the path.

    I started off with the definition of KE: (mv)^2/2 and the fact that a = v^2/r, where F = m(v^2/r).

    Then, I thought;

    mv^2 = 2*KE and mv^2 = F*r so r = (2KE)/F so r^2 = (4KE^2)/ F^2, but this is probably wrong. What should I do if so?

    Thanks.
     
  2. jcsd
  3. Apr 1, 2005 #2
    What do you know about the strength of magnetic fields in relation to distance R?
     
  4. Apr 1, 2005 #3
    If B is constant, then r is constant??
     
  5. Apr 1, 2005 #4
    Well typically one would say that backwards, since B is a function of r. What is B as a function of R?

    What does B have to be equal to to put the particle in uniform circular motion? Think about the force involved in circular motion, and the force of a magnetic field.
     
  6. Apr 3, 2005 #5
    Remember:
    F=mv²/r
    and F=Bqv

    also v=(2pi.r)/t
     
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