Early black-and-white television sets used an electron beam to draw a picture on

Question

Early black-and-white television sets used an electron beam to draw a picture on the screen. The electrons in the beam were accelerated by a voltage of 3.0 kV; the beam was then steered to different points on the screen by coils of wire that produced a magnetic field of up to 0.53T .

Part A

What is the speed of electrons in the beam?

Express your answer to two significant figures and include the appropriate units.

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Part B

What acceleration do they experience due to the magnetic field, assuming that it is perpendicular to their path? What is this acceleration in units of g?

Express your answer using two significant figures.

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Part C

If the electrons were to complete a full circular orbit, what would be the radius?

Express your answer to two significant figures and include the appropriate units.

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Explanation / Answer

Part A

From the conservation of energy, PE = KE

so, qV =0.5mv2

(1.6 X 10-19)(3000) = (0.5)(9.11 x 10-31)(v2)

v = 3.25 X 107 m/s

Part B

F = qvB = ma

(1.6 X 10-19)(3.25 X 107)(0.53) = (9.11 X 10-31)(a)

a = 3.025 X 1018 m/s2 which is 3.084 X 1017 g's

Part C
The formula to find the radius is

r = mv/qB

r = (9.11 X 10-31)(3.25 X 107)/(1.6 X 10-19)(0.53)

r = 3.49 X 10-4 m which is 0.349 mm

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