Charge between parallel plates

[Jrads]

Homework Statement

Given a charge -e moving through a set of charged plates at a velocity of 0.8 x10^7 m/s. The plates have a voltage of 4000v, how long can the plates be without the charge -e impacting one of them?
-e = -1.602 x 10^-6 C
Me = 9.11 x 10^-31 kg

Relevant Equations

E=v/d
F=qE=ma

Electric field between the plates
V=4x10^3
d=0.02
E=4x10^3/0.02
E=2x10^5 V/m

Calculate the force on charge -e
-e = -1.602x10^-6
Me = 9.11x10^-31
F=qE
F=(1.602x10^-6)(2x10^5)
F=0.3204 N

Using F=ma
a=F/Me
a=0.3204/9.11x10^-31
a=3.517x10^29 m/s

Time = distance / speed
T=.01 (half distance of plates with charge in the middle) / 3.517x10^29
T =2.84x10^-32 seconds

Calculate the distance the charge would move at 0.8x10^7 m/s in 2.84x10^-32 seconds

Distance = speed x time
Distance = 0.8x10^7 x 2.84x10^-32
Distance = 2.272x10-25 mtrs
I think I have royally screwed up my calculations somewhere here as a) the charge is moving substantially faster than the speed of light. And b) the length or distance seems really really small?

 

[Steve4Physics]

A few points to consider...

If 'e' is meant to be the elementary charge, then e = 1.602x10⁻¹⁹C, not 1.602x10⁻⁶C.

The particle (it may not be an electron) behaves like a simple projectile, with an initial horizonal velocity, in a gravitational field. Make sure you know how to do simple projectile calculations!

Watch out for careless mistakes. E.g the unit for acceleration is not m/s!

 

[Delta2]

Except the mistake regarding the value of acceleration due to the electric field, which mistake is due to wrong charge of electron as spotted by @Steve4Physics , you have done another mistake in calculating the time to move vertically from the middle up (or down) to the plate due to the electric field.

You should use the formula $$y=\frac{1}{2}at^2$$ and not $$y=at$$ which is the one you used (y=0.01 since that charge starts from middle).