Calculate the force on an electron if the accelerating plates are held at a pote

Question

Calculate the force on an electron if the accelerating plates are held at a potential difference of 600 V. (Note this is V_g.) Assume a distance of 1 cm between the plates. Compare this force, F_e, to the force due to gravity, F_g; i.e., calculate F_g/F_c. Can we safely neglect the effect of gravity in this experiment? For the case above, what is the speed of the electron, upsilon_x, in terms of the speed of light? If upsilon_x > 0.5c (roughly), then Newton's laws begin to break down, and we must use relativistic equations which obey Einstein's theory of relativity. Are relativistic equations necessary in this case? If the electron above passes directly between the pair of parallel plates used in this experiment, what voltage must we apply to the plates to send the electron crashing into one of the plates? (Note, this is V_d.) The electron is initially moving parallel to x the plates equidistant from either plate. How long is the electron "under the influence" of the electric field due to the plates? This is known as the interaction time, t_int = l_eff/upsilon_x; it is often a quantity of interest.

Explanation / Answer

4.

from part 1 of your question

Fg=Fe

ma=qE

a=qE/m

From

Y=Yo+Voyt+(1/2)at2

=>initial Velocity along vertical direction Viy=0

d=(1/2)*(qE/m)*t2

=>t=sqrt(2dm/qE)

Mass of electron

m=9.11*10-31kg

charge of electron q=1.6*10-19C

Electric field

E=V/d=600/0.01=60000 V/m

=>t=sqrt(2*0.01*9.11*10-31/1.6*10-19*60000)

t=1.378*10-9 s

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