Electrons in a television\'s CRT are accelerated from rest by an electric field

Question

Electrons in a television's CRT are accelerated from rest by an electric field through a potential difference of 2.9 kV. In contrast to an oscilloscope, where the electron beam is deflected by an electric field, the beam is deflected by a magnetic field.
    (a) What is the speed of the electrons?
          m/s
    
    (b) The beam is deflected by a perpendicular magnetic field of magnitude 1.03 T. What is the magnitude of the acceleration of the electrons while in the field?
          m/s2
    
    (c) What is the speed of the electrons after they travel 4.5 mm through the magnetic field?
          m/s
    
    (d) What strength electric field would give the electrons the same magnitude acceleration as in (b)?
          V/m

    (e) Why do we have to use an electric field in the first place to get the electrons up to speed? Why not use the large acceleration due to a magnetic field for that purpose?

Explanation / Answer

a)

eV = 1/2 mv^2

V potential difference
m mass of electron
v velocity of electron

v = sq root of 2eV/m = sq root 1.6*10^(-19)*2.5*10^3/9.1*10^(-31)

b)


Bev = mv^2/r B magnetic field, r = radius of circular path taken by the electron in magnetic field.

r = mv/Be


acceleration = v^2/r = substitute v from (a)^2/mv/Be

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