What is the surface charge density of the plane?

[jm21]

I have two problems that I need help working on. The first one is
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 1.0 x 10^7 m/s. What is the surface charge density of the plane?

The second problem is:
A 75.7 nC charge is located at position (x,y) = (1.0 cm, 2.0 cm). At what (x,y) position(s) is the electric field: a) -225,000i N/C b) (161,000i + 85,000j) N/C and c) (21,600i - 28,800j) N/C.

 

[Astronuc]

We ask that students show work.

Since the problem references charged planes, it would seem that one is referring to parallel plate capacitors.

Please try to write the formulas one would use for each problem.

Charges create an electric field, which is a vector field. Free charges accelerate in an electric field. If the electric field is constant, the force on a give charge is constant and the acceleration is therefore constant (assuming non-relativistic dynamics).

 

[jm21]

For the first problem I tried to first find E (the electric field) by using the formula E =Q/2εo(pi)(r^2). I got E to be 1.14 x 10^-11. Then I plugged E into the formula E = sigma/2εo where sigma is the surface density. This turned out to be 2.01 x 10^-22. However, that answer was not right.
I'm not even sure how to approach the second problem. I know you have to do the reverse of what you would do to find the electric field using the formula E=kq^2/r^2.