To solve this problem we will apply the concepts related to voltage as a dependent expression of the distance of the bodies, the Coulomb constant and the load of the bodies. In turn, we will apply the concepts related to energy conservation for which we can find the speed of this
Here,
k = Coulomb's constant
q = Charge
r = Distance to the center point between the charge
From each object the potential will be
Replacing the values we have that
Now the potential two is when there is a difference at the distance of 0.1 from the second charge and the first charge is 0.1 from the other charge, then,
Applying the energy conservation equations we will have that the kinetic energy is equal to the electric energy, that is to say
Here
m = mass
v = Velocity
q = Charge
V = Voltage
Rearranging to find the velocity
Replacing,
Therefore the speed final velocity of the electron when it is 10.0 cm from charge 1 is