An electron is launched into a region of constant electric field, E = 4×104 N/C

Question

An electron is launched into a region of constant electric field, E = 4×104 N/C directed along the positive y axis of a rectangular coordinate system, with an initial velocity of 2.7×107 m/s in the positive x direction. How far has the electron traveled in the y direction during the time interval it takes to move 40 mm in the x direction? (Even though the speed at which the electron moves is an appreciable fraction of the speed of light, ignore relativistic effects.) Express your answer with the appropriate units.

Explanation / Answer

for x direction:
d = 40 mm = 0.04 m
t = d/vx
= 0.04 / (2.7*10^7)
= 1.48*10^-9 s

in y direction,
acceleration, a = q*E/m
= (1.6*10^-19)*(4*10^4) / (9.1*10^-31)
= 7.03*10^15 m/s^2

vi = 0 m/s

d = vi*t + 0.5*a*t^2
= 0*(1.48*10^-9 ) + 0.5*(7.03*10^15 )*(1.48*10^-9 )^2
=0.5*(7.03*10^15 )*(1.48*10^-9 )^2
= 7.7*10^-3 m
= 7.7 mm

Answer: 7.7 mm

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