A beam of electrons is shot into a uniform downward electric field of magnitude

Question

A beam of electrons is shot into a uniform downward electric field of magnitude 1.09 103 N/C. The electrons have an initial velocity of 1.10 107 m/s, directed horizontally. The field acts over a small region, 5.00 cm in the horizontal direction.
(a) Find the magnitude and direction of the electric force exerted on each electron.
magnitude= ?
direction= ?



(c) How far has each electron moved in the vertical direction by the time it has emerged from the field?


(d) What is the electron's vertical component of velocity as it emerges from the field? (Up is the positive y-direction.)


(e) The electrons move an additional 19.2 cm after leaving the field. Find the total vertical distance that they have been deflected by the field.

Explanation / Answer

E = 1.09 x10^3= 1.09 e3
and v = 1.10 x10^7 = 1.10 e7

a) force on the e- , use: E= F/q
F= qE = (1.602 e-19C) * (1.09 x10^3 NC-1 )
F= 1.75 x10^-16 N

c) so that force is exerted on the e-, use F=ma to find the 'a'
use the x-component velocity 1.10e7 to find the time the electron is in between the plates
t= x/v = .05m/1.10e7 = 4.54e-9 seconds
a= F/m = 1.75e-16N/ (9.11e-31kg)= 1.92 e14 ms-2
then use: y= y0 +v0t + 1/2 at^2
v0t= 0 because initially there isn't any velocity in the y-dxn
y0= doesn't really matter because it's a uniform field, just set it to 0 as a reference pt
y= 1/2 (1.92e14)(4.54e-9)^2
t= 1.97e-3m or .19 cm upwards

d) v =v0+ at= 0ms-1 + 1.92e14 ( 4.54e-9)
v= 8.71 x10^5 ms-1

e) so after the e- has left the field, it's path will be straight & diagonally upward, it still has it's original x-component, however it also has a y-component (the difference is , that in the field there is constant force so it was curved upwards)

basically the distance is x^2 +y2= .192^2
the distance in x -dxn is Vx (t) and Vy(t) in y-dxn
you get (Vx*t)^2 + (Vy*t)^2= .192^2
solve for 't' using the original x- velocity , and the final y-velocity
t^2 = .192^2 / [ (1.10e7)^2 + (8.71 x10^5 )^2]

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