Electron Approaching a Charged Sphere

[jrk012]

Homework Statement

An electron starts from rest 2.80 cm from the center of a uniformly charged sphere of radius 1.83 cm. If the sphere carries a total charge of 1.01×10-9 C, how fast will the electron be moving when it reaches the surface of the sphere?

Homework Equations

UI + KI = UF + KF
U=(k*Q*-e)/r
K=1/2mv^2

The Attempt at a Solution

Rearranging terms I got:

[([(k*Q*-e)/(r-initial)] - [(k*Q*-e)/(radius)])/(r-initial - radius)](2/m)

Using:
k = 9x10^9
Q = 1.01×10-9
e = 1.602 x 10^(-19)
m = 9.1094 x 10^(-31)
r-initial = .028m
radius = .0183m

I then get v^2 = 6.24x10^15. I square root(√) it to get v and I get:

v = 7.9x10^7 m/s

I have tried the negative and positive of this and I cannot solve it. Any help would be appreciated

 

[SammyS]

Homework Statement

An electron starts from rest 2.80 cm from the center of a uniformly charged sphere of radius 1.83 cm. If the sphere carries a total charge of 1.01×10-9 C, how fast will the electron be moving when it reaches the surface of the sphere?

Homework Equations

UI + KI = UF + KF
U=(k*Q*-e)/r
K=1/2mv^2

The Attempt at a Solution

Rearranging terms I got:

[([(k*Q*-e)/(r-initial)] - [(k*Q*-e)/(radius)])/(r-initial - radius)](2/m)

Using:
k = 9x10^9
Q = 1.01×10-9
e = 1.602 x 10^(-19)
m = 9.1094 x 10^(-31)
r-initial = .028m
radius = .0183m

I then get v^2 = 6.24x10^15. I square root(√) it to get v and I get:

v = 7.9x10^7 m/s

I have tried the negative and positive of this and I cannot solve it. Any help would be appreciated

What is the factor, (r-initial - radius) doing in there?

 

[jrk012]

SammyS, you are a saint. Thank you!