4. A schematic of a cathode ray tube is shown below. We\'ll assume that the x-de

Question

4. A schematic of a cathode ray tube is shown below. We'll assume that the x-deflection plates are inactive (so that they do not affect the electron beam) and ignore them. Follow the steps below to calculate the deflection of the electron beam in the y-direction. Idi a. (l p) If the voltage difference between the front and back of the main body of the CRT is V, and the length of the tube is L, calculate the magnitude of the electric field in the z-direction and use your expression for E, to show that az b. (1 pt) Assuming this acceleration is constant and that the electrons were initially at rest, use the kinematic equations to show that when the electrons have traveled a distance L their speed is

Explanation / Answer

a)

Electric field is given as

E = Vz/L1

Electric force is given as

F = q E = q Vz/L1

using newton's second law

ma = F =  q Vz/L1

a = q Vz/(mL1)

b)

using the equation

Vf2 = Vi2 + 2 a L1

Vf2 = 02 + 2 (q Vz/(mL1)) (L1)

Vf = sqrt(2q Vz/m)

c)

w = width of plate

Vf = sqrt(2q Vz/m)

time is given as

t = w/Vf = w/sqrt(2q Vz/m) = w sqrt(m/(2q Vz))

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