The electron beam inside a television picture tube is 0.400 mm in diameter and c

Question

The electron beam inside a television picture tube is 0.400 mm in diameter and carries a current of 55.0 A. This electron beam impinges on the inside of the picture tube screen.

Part B: What is the current density in the electron beam? Answer needs to be in A/m^2.

Part C: The electrons move with a velocity of 4.30 ×107m/s. What electric field strength is needed to accelerate electrons from rest to this velocity in a distance of 4.60 mm ? Answer needs to be in N/C.

Part D: Each electron transfers its kinetic energy to the picture tube screen upon impact. What is the powerdelivered to the screen by the electron beam? Answer needs to be in W.

Explanation / Answer

A. Current density J = Current/area = i/A

J = 55 e -6/(3.14 * 0.2 e-3 * 0.2e -3)

J = 437.89 A/m^2

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use ma = Eq

here a = v^2/2S = (4.3 e7 * 4.3 e 7)/(2* 4.6 e -3)

a = 2e 17 m/s^2

so E = ma/q

E = 9.11 e -31* 2 e 17/(1.6 e -19)

E = 1.14 *10^6 N/C

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Power P = Vi

here V = Ed

so power P = 1.14 e 6 * 4.6 e -3 * 55 e-6

P = 0.288 Watts

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