As electrons (charge phi = -1. 6 times 10 -19 C, mass m1 = 9. 1 times 10-31 is p

Question

As electrons (charge phi = -1. 6 times 10 -19 C, mass m1 = 9. 1 times 10-31 is projected at an initial speed of v1 = 1. 5 times 106 m/s, at angle theta1 = 45 degree from an x-axis, as shown. It moves through a uniform electrical field E = (65. 0 N/C)J. A screen for detecting electrons is positioned to the y-axis, at distance x = 4. 5 cm. Neglect gravity. Find the time t it taken the electron to reach the screen. Find the components v0 v1 of its velocity at impact on the screen. Find the y-component of the impact point.

Explanation / Answer

q = 1.6e-19

m = 9.1e-31

v = 1.5e6

= 45

E = 65 N/C

x = 4.5 cm

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a)

t = x/vx

t = 0.045/(1.5e6cos45)

t = 0.045/(1.5e6*0.70711)

t = 4.2426e-8

t = 4.24e-8 s

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b)

vx = 1.5e6cos45 = 1.5e6*0.70711 = 1.0607e6

vx 1.06e6 m/s

vy = a t + v sin45 = -eEt/m + v sin45

vy = -1.6e-19*65*4.2426e-8/9.1e-31 + 1.5e6*0.70711

vy = 0.57580e6 m/s

vy 0.576e6 m/s

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c)

y = - 0.5 a t^2 + v sin45 t

y = 0.5 * (-1.6e-19*65*4.2426e-8*4.2426e-8/9.1e-31) + 1.5e6*0.70711*4.2426e-8

y = 0.0347 m

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