(a) Amonoenergetic electron beam with electron speed of 5.20 × 106m

1.	(a) Amonoenergetic electron beam with electron speed of 5.20 × 106m s−1is subject to a magnetic field of 1.30 × 10−4T normal to the beam velocity. What is the radius of the circletraced by the beam, given e/m forelectron equals 1.76 × 1011C kg−1.(b) Is theformula you employ in (a) valid for calculating radius of the path ofa 20 MeV electron beam? If not, in what way is it modified?[Note:Exercises 11.20(b) and 11.21(b) takeyou to relativistic mechanics which is beyond the scope of this book.They have been inserted here simply to emphasise the point that theformulas you use in part (a) of the exercises are not valid at veryhigh speeds or energies. See answers at the end to know what ‘veryhigh speed or energy’ means.]
Answer» (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 × 10¹¹ C 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 emphasise 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.]

(a) Amonoenergetic electron beam with electron speed of 5.20 × 106m s−1is subject to a magnetic field of 1.30 × 10−4T normal to the beam velocity. What is the radius of the circletraced by the beam, given e/m forelectron equals 1.76 × 1011C kg−1.(b) Is theformula you employ in (a) valid for calculating radius of the path ofa 20 MeV electron beam? If not, in what way is it modified?[Note:Exercises 11.20(b) and 11.21(b) takeyou to relativistic mechanics which is beyond the scope of this book.They have been inserted here simply to emphasise the point that theformulas you use in part (a) of the exercises are not valid at veryhigh speeds or energies. See answers at the end to know what ‘veryhigh speed or energy’ means.]

Answer»

(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 × 10¹¹
C 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 emphasise 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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