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 2300 N/C . The electric field covers a region of space 12.5 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.

Explanation / Answer

here,

electric feild , E = 2300 N/C

d = 0.125 m

a)

the accelration , a = E * q /m

a = 2300 * 1.6 * 10^-19 /(9.1 * 10^-31)

a = 4.04 * 10^14 m/s^2

the speed of the electron , v = sqrt(2 * a * d)

v = sqrt(2 * 4.04 * 10^14 * 0.125)

v = 1 * 10^7 m/s

b)

let the time taken be t

v = u + a * t

1 * 10^7 = 4.04 * 10^14 * t

t = 2.49 * 10^-8 s

the fall under the influence of gravity , y = 0 + 0.5 * g * t^2

y = 0.5 * 9.8 * (2.49 * 10^-8)^2

y = 3.03 * 10^-15 m

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