As an example of the manipulation of an electron beam, consider an electron trav

Question

As an example of the manipulation of an electron beam, consider an electron traveling away from the origin along the x axis in the xy plane with initial velocity . As it passes through the region x = 0 to x = d, the electron experiences acceleration , where ax and ay are constants. For the case vi = 1.90 ? 107 m/s, ax = 7.51 ? 1014 m/s2, and ay = 1.51 ? 1015 m/s2, determine the following, at x = d = 0.0100 m. the position of the electron the velocity of the electron the speed of the electron the direction of travel of the electron (i.e. the angle between its velocity and the x axis)

Explanation / Answer

the initial position (0, 0)
the final position (d, yf)
so the displacement r = (d, yf)
the initial velocity (vi, 0)
the final velocity (vx, vy)
the acceleration (ax, ay)
since ax is constant,
d = vi*t + ax*t^2/2
ax*t^2/2 + vi*t - d = 0
t = [-vi + sqrt(vi^2 + 2ax*d)]/ax
= 4.64 x 10^(-8) s

a) yf = ay*t^2/2 = 1.59 m
b) vx = vi + ax*t = 5.02 x 10^7 m/s
vy = ay*t = 6.89 x 10^7 m/s
so vf = (5.02 x 10^7, 6.89 x 10^7)m/s
c) v = sqrt(vx^2 + vy^2) = 8.52 x 10^7 m/s
d) angle with +X direction = arctan(vy/vx) = 53.9

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