A cathode ray tube is used to accelerate electrons in x-ray tubes and other devi

Question

A cathode ray tube is used to accelerate electrons in x-ray tubes and other devices. Electrons from a heated filament pass through a hole in the cathode, they are then accelerated by an electric field between the cathode and the anode (see Fig. 16.39 in your textbook). Suppose an electron passes through the hole in the cathode at the initial velocity of 104.4 km/s toward the anode. The electric field is uniform between the anode and cathode. The anode and the cathode are separated by 1.2 cm, and after traversing that distance the electron reaches the final velocity of 6261.5 km/s

What is the magnitude of the uniform electric field between the anode and cathode?

Explanation / Answer

Given,

v1 = 104.4 km/s = 104.4 x 10^3 m/s

v2 = 6261.5 km/s = 6261.5 x 10^3 m/s

d = 1.2 cm = 0.012 m

The work done by the electric field is given by:

U = q E d

This will be equal to the change in kinetic energy

q E d = 1/2 m (v2^2 - v1^2)

E = m/2 q d (v2^2 - v1^2)

E = 9.1 x 10^-31/(2 x 1.6 x 10^-19 x 0.012) [ (6261.5 x 10^3)^2 - (104.4 x 10^3)^2] = 9288.513 N/C

Hence, E = 9288.51 N/C

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