- #1

- 1,380

- 22

## Homework Statement

Two electrons are held at rest 0.05[cm] apart. what is their relative velocity when they are 1[cm] apart.

## Homework Equations

The potential V from a point charge: ##V=K\frac{q}{r}##

The constant ##K=9\cdot 10^9##

The work done to move from one point in the field to another: ##W=V\cdot q##

The electron charge: ##e=1.6\cdot 10^{-19}[Coulomb]##

The electron mass: ##m_e=9.11\cdot 10^{-31}[Kg]##

## The Attempt at a Solution

The axes are attached to one of the electrons. the potential difference between the end and the beginning:

$$\Delta V=9\cdot 10^9\cdot 1.6\cdot 10^{-19}\cdot \left(\frac{1}{0.0005}-\frac{1}{0.01}\right)=2.7\cdot 10^{-6}$$

The work is the gained kinetic energy:

$$W=E_k=2.7\cdot 10^{-6}\cdot 1.6\cdot 10^{-19}=4.378\cdot 10^{-25}=\frac{1}{2}\cdot 9.11\cdot 10^{-31}\cdot V^2\rightarrow V=0.0023[m/s]$$

It should be 982[m/s]