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20 February, 22:45

In a certain cyclotron a proton moves in a circle of radius 0.670 m. The magnitude of the magnetic field is 1.30 T. (a) What is the oscillator frequency? (b) What is the kinetic energy of the proton?

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  1. 20 February, 23:41
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    a) The formula for a cyclotron's frequency:

    f = (qB) / (2πm)

    f is the frequency, q is the particle's charge, B is the magnetic field strength, and m is the particle's mass.

    Given values:

    q = 1.6*10⁻¹⁹C (proton charge)

    B = 1.30T

    m = 1.67*10⁻²⁷kg (proton mass)

    Plug in these values and solve for f:

    f = (1.6*10⁻¹⁹*1.30) / (2π*1.67*10⁻²⁷)

    f = 1.98*10⁷Hz

    b) The kinetic energy of a particle in the cyclotron is:

    KE = 0.5q²B²r²/m

    q is the particle's charge, B is the magnetic field strength, r is the radius of the particle's path, and m is the particle's mass.

    Given values:

    q = 1.6*10⁻¹⁹C (proton charge)

    B = 1.30T

    r = 0.670m

    m = 1.67*10⁻²⁷kg (proton mass)

    Plug in the values and solve for KE:

    KE = (0.5) (1.6*10⁻¹⁹) ² (1.30) ² (0.670) ²/1.67*10⁻²⁷

    KE = 5.81*10⁻¹²J
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