Calculate Speed of Electron from Charge Density

[tony873004]

** Edit: Nevermind. I figured it out using the Work Energy theorem.

An electron is released from rest 1.0 cim above a uniformly charged infinite plane with a charge density of 10^-9C/m². What is the speed of the electron when it hits the plane?

my attempt:
Potential energy when it is released= kinetic energy when it hits.

kqQ/r = 0.5 mv²

isolate v:

<br /> v = \sqrt {\frac{{2kqQ}}{{m \cdot r}}} <br />

This would work if I was given 2 point charges, but how do I do this with a charge density and a point charge?

 

[member 553083]

Answer:The speed of the electron when it hits the plane can be calculated using the equation v = √(2kqQ/mr), where q is the charge of the electron, Q is the charge density of the plane, and m is the mass of the electron. In this case, q=1.6x10-19 C, Q=10-9 C/m2, and m=9.1x10-31 kg. Plugging in these values gives a speed of 1.9x106 m/s.