Electrostatics and infinately charged plate question driving me nuts

[ursulan]

Homework Statement

An electron is released from rest 2.0 cm from an infinite charged plane. It accelerates toward the plane and collides with a speed of 1.0x10^7m/s. What is the surface charge density of the plane?The answer is 2.52×10−7 C/m^2 !

Homework Equations

v=d/t, d=0.5at^2, E=n/2*8.85x10^-12, F=ma=Eq

The Attempt at a Solution

I don't know what to do with the velocity. I tried relating it to energy but got stuck.

 

[Doc Al]

I don't know what to do with the velocity.

Use that and the distance to find the electron's acceleration.

 

[ursulan]

using v=d/t t is 2E-9
using a=v/t a is 5E15
E=ma/q E=28469
E=n/(2 epsilon not).. n=5.03E-7

which is 2 times too big, but isn't E=n/(2 epsilon not) the correct equation, with the 2?

 

[Doc Al]

using v=d/t t is 2E-9

That equation applies for constant velocity, not accelerated motion. But you can use it if you replace v (the final velocity) with the average velocity. What's the average velocity?

You can also make use of additional kinematic relationships.

 

[ursulan]

ahh so I guess you mean Vf^2=V0^2 + 2ad because that works haha

Thanks!

 

[Doc Al]

That's the one.