In Prob. 12.63, determine the smallest allowable value of the ratio d/l in terms of e, m, v0, and…

In Prob. 12.63, determine the smallest allowable value of the ratio d/l in terms of e, m, v0, and V if at x =  the minimum permissible distance between the path of the electrons and the positive plate is 0.05d. 12.65 The current model of a cathode-ray tube is to be modified so that the length of the tube and the spacing between the plates are reduced by 40 percent and 20 percent, respectively. If the size of the screen is to remain the same, determine the new length of the plates assuming that all of the other characteristics of the tube are to remain unchanged

Prob. 12.63 In the cathode-ray tube shown, electrons emitted by the cathode and attracted by the anode pass through a small hole in the anode and then travel in a straight line with a speed 0 until they strike the screen at A. However, if a difference of potential V is established between the two parallel plates, the electrons will be subjected to a force F perpendicular to the plates while they travel between the plates and will strike the screen at point B, which is at a distance d from A. The magnitude of the force F is F = e/d, where 2e is the charge of an electron and d is the distance between the plates. Derive an expression for the deflection d in terms of V, 0, the charge 2e and the mass m of an electron, and the dimensions d, l, and L.