Displacement of an electron between two plates

[oy_katet]

Homework Statement

In an oscilloscope, an electron is accelerated from rest through a voltage of 1.14x10³ V. It then passes through deflecting plates 2.00 cm apart, across which there is a voltage of 412 V. Its velocity when it enters the plates is perpendicular to the electric field of the plates. When the electron leaves the plates, what distance will it have moved toward the positive plate? The length of the plates are 4.00 cm.

The answer is 7.23x10^-3 m

Homework Equations

Givens:
v_i= 0
V_a= 1.14x10³ V
V_d= 412 V
length of plate = 4 cm = 0.04 m
d= 2 cm= 0.02 m

Equations:
1/2mv²= V_aq
t=length of plate/v
E=V_d/d
F= Eq
a= F/m
x=1/2at²

The Attempt at a Solution

So, because it's an electron
q= 1.6x10^-19
m= 9.11x10^-31

Using the above equations and plugging in the givens, I've gotten:

v= 2.001x10⁷ m/s

t=1.0x10^-9 s

E= 20600 v/m

F= 3.296x10^-15 N

a= 3.618x10¹⁵ m/s²

x= 1.809x10^-3 m


which is not the right answer :( I'm not very good at physics so I'm having a hard time figuring out what I'm doing wrong.

 

[ehild]

Using the above equations and plugging in the givens, I've gotten:

v= 2.001x10⁷ m/s

Correct...

t=1.0x10^-9 s

here is a mistake: The electron travels along the length of the plate with the v=2.00 m/s so the time is 2.0x10^-9 s

ehild

 

[oy_katet]

Correct...



here is a mistake: The electron travels along the length of the plate with the v=2.00 m/s so the time is 2.0x10^-9 s

ehild

Wellp, I'm just a big ol' dummy! I can't believe I made that oversight. Thanks so much!