In an x-ray tube, electrons are accelerated in a uniform electric field and then

Question

In an x-ray tube, electrons are accelerated in a uniform electric field and then strike a metal target. Suppose an electron starting from rest is accelerated in a uniform electric field directed horizontally and having a magnitude of 3000 N/C . The electric field covers a region of space 10.5 cm wide.

Part A

What is the speed of the electron when it strikes the target?

Express your answer with the appropriate units.

Part B

How far does it fall under the influence of gravity during its flight?

Express your answer with the appropriate units.

Comment

Explanation / Answer

(a) force F = E*q = 3000N/C * 1.6e-19C = 4.8 e-16 N
acceleration a = F / m = 4.8e-16N / 9.11e-31kg = 5.27e14 m/s²
Then v² = u² + 2as = 0 + 2 * 5.27e14m/s² * 0.105m = 1.1067e14 m²/s²
and v = 1.05e7 m/s

(b) time t = d / v = 0.105m / 1.05e7m/s = e-8 s
so it falls distance d = ½at² = ½ * 9.8m/s² * (e-8s)² = 4.9e-16 m

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