The electrons in a cathode ray tube are emitted by a hotfilament cathode and are accelerated by an electric field appliedbetween the cathode and two orthogonal pairs of parallel plateelectrodes. The beam passes through the gap between the electrodesand can be deflected up and down, or left and right if the parallelplates are appropriately biased. As the electrons pass through theelectrodes, their kinetic energy increases. Assume the electronsare emitted from the cathode with a thermal velocity correspondingto a temperature of 3000 °C, are accelerated through a potential of5000 V over a distance of 10 mm and then travel horizontally over adistance of 200 mm before they are collected on the phosphor-coatedsurface of the display screen. (a) Write the equation of motion forthe electrons. Assume the electric field acts only in thex-direction between the cathode and the plates. (b) Calculate thevelocity of the electrons after they have been electrostaticallyaccelerated. (c) Calculate the downward deflection of the electronsover the 200 mm gap caused by the gravitational force acting in thenegative y-direction. Use Vthermal = (8kT/pi*m)1/2 where m is themass of the electron.
