Electron in an oscilloscope **
The deflection plates in a high-voltage cathode ray oscilloscope are two rectangular plates, 4 cm long and 1.5 cm wide, and spaced 0.8 cm apart. There is a difference in potential of 6000 V between the plates. An electron that has been accelerated through a potential difference of 250 kV enters this deflector from the left, moving parallel to the plates and halfway between them, initially. We want to find the position of the electron and its direction of motion when it leaves the deflecting field at the other end of the plates. We shall neglect the fringing field and assume the electric field between the plates is uniform right up to the end. The rest energy of the electron may be taken as 500 keV.
((a)) First carry out the analysis in the lab frame by answering the following questions:
• What are the values of γ and β?
• What is px in units of mc?
• How long does the electron spend between the plates? (Neglect the change in horizontal velocity discussed in Exercise 5.25.)
• What is the transverse momentum component acquired, in units of mc?
• What is the transverse velocity at exit?
• What is the vertical position at exit?
• What is the direction of flight at exit?
((b)) Now describe this whole process as it would appear in an inertial frame that moved with the electron at the moment it entered the deflecting region. What do the plates look like? What is the field between them? What happens to the electron in this coordinate system? Your main object in this exercise is to convince yourself that the two descriptions are completely consistent.