6. An electron flies with speed tn-1.1 x 101 into a uiform electrie field E 0.2g

Question

6. An electron flies with speed tn-1.1 x 101 into a uiform electrie field E 0.2g between parallel plates, as show n in the figure. The pirallel plates are separated by n distance d= 2 mm, and the electron entry point is exactly midway between the plates at (Ignore gravity for this problem, and assune that the plates extend far enough to the right that the electron will eventually strike one of them.) 44444 + -12 C di2 a. Calculate the surface charge density on the top plate. . Find the magnitude of the electrie potential between the plates. 2 C. Calculate the change in electric potential energy of the electron from its starting entry point at to where it hits one of the plates. Indicate which direction the electron would be deflected. d. Calculate the final velocity with which the electron hits the appropriate plae

Explanation / Answer

part a )

E =sigma/eo

sigma = E*eo

sigma = 1.77 x 10^-12

part b )

V = E.d

d = 2mm = 2 x 10^-3 m

V = 4 x 10^-4 V

part c )

dV = E*(d/2) = 2 x 10^-4 V

U = qdV

U = -1.6 x 10^-19 x 2 x 10^-4 = -3.2 x 10^-23 J

part d )

using energy conservation

Ki + Ui = Kf + Uf

kf = ki - (Uf-Ui)

Kf = 1/2 * mv^2 + 3.2 x 10^-23

kf = 1/2 * 9.11 x 10^-31 * (1.1*10^4)^2 + 3.2 x 10^-23

kf = 8.71155 x 10^-23

1/2*mvf^2 = 8.71155 x 10^-23

vf = 1.38 x 10^4 m/s

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