An electron falls through a distance of 1.5 cm in a uniform electric field of magnitude 2x10^{4 N/C} .What is the time of fall.

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Solution

Mass of electron= 9.1 10^ -31 kg
Distance, d= 1.5cm=0.015 m
Electric field intensity, E= 210^ 4 N/C
Charge of electron , q= 1.610^ -19 C

We have force due to electric field balances force due to mass of body
F electric= F
qE= ma
a= qE/m = 1.610^ -19* 210^ 4 / 9.1 10^ -31 = 3.5210^ 15 m/s^2

since it falls, we take it's initial velocity as , Vi=0 m/s
d= Vi t+1/2at^2
d= 1/2at^2
0.015 = 1/2* 3.5210^ 15 t^2
0.015= 1.7610^ 15 t^2
0.015 / 1.7610^ 15= t^2
t^2= 8.510^ 12
t= 2.92*10^ 6 s

Time of fall is **2.92*10^ 6 s**

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