The electron beam inside a television picture tube is 0.40 mm in diameter and ca

Question

The electron beam inside a television picture tube is 0.40 mm in diameter and carries a current of 50 micro-A This electron beam impinges on the inside of the picture tube screen.

a) How many electrons strike the screen each second?
(2 sig figs)

b)The electrons move with a velocity of 4.0*10^7 m/s. What electric field strength is needed to accelerate electrons from rest to this velocity in a distance of 5.0 mm?
(2 sig figs)

c) Each electron transfers its kinetic energy to the picture tube screen upon impact. What is the power delivered to the screen by the electron beam? (Hint: What potential difference produced the field that accelerated electrons? This is an emf.)
(2 sig figs)

Explanation / Answer

a) electric current is defined as the charge that passes a given point per second.

I = Q/t

For 50 A, 50C of charge would strick the screen each second.

Each electron has a charge of 1.6*10^-19C. The total charge would equal:

Q = n(1.6*10^-19C) , where n is the number of electrons

50 * 10^-6 C = n (1.6*10^-19C)

n = 3.125*10^14

That's how many electrons hit the screen each second.

b) The work done in moving a charged particle in an electric field is:

W = qEd, because electric force is qE and d would be the displacement. Each electron has a charge of 1.6*10^-19C. So,

W = (1.6*10^-19C)E(0.005m)

W = (8*10^-22)E, where E is the strenght of the electric field.

Any time work is done on an object, its kinetic energy changes.

W = K = Kf-Ki

Its initial kinetic energy is 0, so

W = Kf = (0.5)mv^2

Each electron has a mass of 9.11*10^-31kg.

(8*10^-22)E = (0.5)(9.11*10^-31kg)(4.0*10^7m/s)^2

E = 911000 N/C

c) *not sure if this is the way that they want it done but it will work

Each electron has a kinetic energy of (0.5)(9.11*10^-31kg)(4.0*10^7m/s)^2 = 7.288*10^-16 J

and there are 3.125*10^14 of them hitting the screen each second.

The total amount of kinetic energy being transferred to the screen each second is then:

3.125*10^14*(7.288*10^-16 J) = 0.22775 J

Power is the rate at which energy is transferred over time so,

P = E/t

P = (0.22775 J)/1s = 0.22775W

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