11.21 (a) A monoenergetic electron beam with electron speed of 5.20 × 106 m s –1 is subject to a magnetic field of 1.30 × 10–4 T normal to the beam velocity. What is the radius of the circle traced by the beam, given e/m for electron equals 1.76 × 1011C kg–1.

(b) Is the formula you employ in (a) valid for calculating radius of the path of a 20 MeV electron beam? If not, in what way is it modified?

[Note: Exercises 11.20(b) and 11.21(b) take you to relativistic mechanics which is beyond the scope of this book. They have been inserted here simply to emphasize the point that the formulas you use in part (a) of the exercises are not valid at very high speeds or energies. See answers at the end to know what ‘very high speed or energy’ means.]

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    Answered by

    Payal Gupta | Contributor-Level 10

    4 months ago

    11.21 Speed of the electron, v = 5.20 ×106m/s

    Magnetic field experienced by the electron, B = 1.30 ×10-4 T

    Specific charge of electron, e/m = 1.76 ×1011 C/kg

    Charge of an electron e = 1.60 ×10-19 C

    Mass of electron, m = 9.1 ×10-31 kg

    The force exerted on the electron is given as

    F = ev?+B?

    evBsin?θ , where θ = angle between the magnetic field and the beam velocity

    The magnetic field is normal to the direction of beam, hence θ=90°

    Therefore, F=evB ………………(1)

    The beam traces a circular path of radius r. The magnetic field due to its bending nature provides a centrifugal forc

    ...more

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