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

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.

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