- #1

Potatochip911

- 318

- 3

## Homework Statement

What is the

*escape speed*for an electron initially at rest on the surface of a sphere with a radius of 1.0 cm and a uniformly distributed charge of ##1.6\times 10^{-15}##? That is, what initial speed must the electron have in order to reach an infinite distance from the sphere and have zero kinetic energy when it gets there?

## Homework Equations

##U_0+K_0=U_f+K_f##

##U=k\frac{q_1q_2}{r}##

## The Attempt at a Solution

$$U_0+K_0=U_f+K_f\Longrightarrow U_0+K_0=0+0\Longrightarrow K_0=-U_0 \\

\frac{1}{2}mv^2=-k\frac{q_1q_2}{r} \\

v=\sqrt{-2k\frac{q_1q_2}{mr}}$$

This is the correct answer but I'm confused a bit as to the radius ##r##, in my textbook it states that in the formula for potential energy, ##U=k\frac{q_1q_2}{r}## that ##r## is the separation between the two particles, however in the answer they plug in ##r=0.01m##, but I would think that the separation between the electron and the sphere is ##0## since the electron is initially at rest on the surface of the sphere (I also don't understand how it can have initial kinetic energy if it's at

*rest*on the sphere).