Label the final answers so I know which one is which. And please show steps. Cha
ID: 1524216 • Letter: L
Question
Label the final answers so I know which one is which. And please show steps. Chapter 22, Problem 040 An electron with a speed of 3.82 x 108 cm/s in the positive direction of an x axis enters an electric field of magnitude 2.63 x 103 N/C, traveling along a field line in the direction that retards its motion. (a) How far wil the electron travel in the field before stopping momentarily, and (b) how much time will have elapsed? (c) If the region containing the electric field is 4.15 mm long (too short for the electron to stop within it), what fraction of the electron's initial kinetic energy will be lost in that region? units (a) Number Number (b) (c) Number units
Explanation / Answer
(A) Vi = 3.82 x 10^8 cm/s = 3.82 x 10^6 m/s
a = q E / m = - (1.6 x 10^-19) (2.63 x 10^3) / (9.109 x 10^-31)
a = - 4.62 x 10^14 m/s^2
Vf = 0
Applying vf^2 - vi^2 = 2 a d
0^2 - (3.82 x 10^6)^2 = 2(-4.62 x 10^14) (d)
d = 0.0158 m Or 15.8 mm
(B) vf = vi + a t
t = 8.27 x 10^-9 sec
(c) Initial KE = (9.109 x 10^-31) ( 3.82 x 10^6)^2 / 2 = 6.646 x 10^-18 J
Kinetic energy lost = q deltaV = q E d
= (1.6 x 10^-19) ( 2.63 x 10^3) ( 4.15 x 10^-3)
= 1.746 x 10^-18 J
fraction of KE lost = (1.746)/ (6.646) = 0.263
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