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Homework Help: Proton in Magnetic field - am I correct?

  1. Jan 19, 2004 #1
    Proton in Magnetic field -- am I correct?

    One of my Physics ISU questions is as follows:
    - A proton moves in a circular path perpendicular to a 1.10 T magnetic field. The radius of the path is 4.5 cm. calculate energy of the proton in eV

    Well i had hard time doing it but here we go: my solution

    mV^2/r=QrB V=QrB/m

    V= (1.6x10^-16) x o.o45 m x 1.10 T) / 1.67x10^-27 kg

    V= 4.7x10^6 m/s

    Ek= 1/2mV^2 = 1/2 x 1.67x10^-27 kg x (4.7x10^6 m/s)^2
    = 1.8x10^-14 J

    Ek= 1.87x10^-14J x eV/1.6x10^-19J = (1.87x10^-14J)/ (1.6x10^-19J)

    eV=1.3x10^5 eV=1.3x10^5

    Fellow physisists is my solution correct?

    Thank you
  2. jcsd
  3. Jan 19, 2004 #2
    Hmm...I got close to 1.17*10^5 eV

    Here's how I did it:

    We want to know the kinetic energy of the proton, so:


    We know the mass of a proton is 1.67*10^-27, so the variable we need is the velocity at which it is travelling.

    As this proton is moving in a circle in a magnetic field,

    [tex]F_m=F_c[/tex] (where [tex]F_m[/tex] is the magnetic force and [tex]F_c[/tex] is the centripetal force

    representing these with equations, we have


    now, we isolate v, since that is what we are trying to get


    substituting into the kinetic energy equation, we get


    which reduces to


    substituting in,


    which gets 1.878*10^-14 J

    since 1 eV = 1.6*10^-19 J, the answer in eV is

    (1.878*10^-14)/(1.6*10^-19) = 117,375 eV (1.17*10^5)

    There are two things about yours that confuse me. First off, the magnitude of the charge on a proton is the elementary charge, which is 1.6*10^-19, whereas you have it as 1.6*10^-16...and yet you get the same energy in joules. Then at the end when you do your conversion from joules to electron volts, there seems to be a discrepency of some kind, because (1.87*10^-14)/(1.6*10^-19) does not equal 1.3*10^5. Also, I would have rounded to 1.88*10^5 if I were rounding. Apart from that the solution the same as mine.
    Last edited: Jan 19, 2004
  4. Jan 19, 2004 #3
    Ok I'll look more into it

    thanks a bunch, help is always appreciated

    BTW that -16... I just copied it wrong from my notes:smile:

    Hmm also you must've read my first post wrong since

    Ek= 1.87x10^-14J x eV/1.6x10^-19J = (1.87x10^-14J)/ (1.6x10^-19J)

    eV=1.3x10^5 eV=1.3x10^5
    Last edited: Jan 19, 2004
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