In Prob. 12.64, determine the smallest allowable value of the ratio d/?? 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 0.075d. Problem 12.64: 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 v0 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 δ from A. The magnitude of the force F is F = eV/d, where ??e is the charge of an electron and d is the distance between the plates. Neglecting the effects of gravity, derive an expression for the deflection δ in terms of V, v0, the charge ??e and the mass m of an electron, and the dimensions d, ??, and L.

Anode Cathode Screen L I