Depth of conventional large screen TV: Assume that in a CRT tube, electrons have

Question

Depth of conventional large screen TV: Assume that in a CRT tube, electrons have initial kinetic energy of 4.00 × 10^16 J. The electron gun in the CRT tube is directly behind the centre of the screen, the electrons have an initial velocity perpendicular to the screen and then pass through a 4.00 cm long gap between two parallel electrodes. The maximum magnitude of electric field E = 5.00 × 10^4 N/C between these plates is required to deflect the electrons to the electrons to the edge of the screen. What is the required distance from the edge of the parallel plates to the screen for the electrons to be able to reach the edge of a screen that is 3.00 ft in width. (Assume electric field is constant everywhere between the plates and zero everywhere outside the plates.)

Explanation / Answer

initial kinetic energy = 4 x 10^-16 J

so, 1/2 x 9.1 x 10^-31 x v^2 = 4 x 10^-16

so, v = 2.96 x 10^7 m/s

time required to cross the gap = 4 x 10^-2 / ( 2.96 x 10^7) = 1.35 x 10^-9 s

acceleration of electron = charge of electron x electric field / mass of electron = 1.6 x 10^-19 x 5 x 10^4/(9.1 x 10^-31) = 8.79 x 10^15 m/s^2

deflection = 1/2 x 8.79 x 10^15 x (1.35 x 10^-9)^2= 8.009 x 10^-3 m = 0.008 m=0.8 cm

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