Question

Two stationary positive point charges, charge 1 of magnitude 3.85 nC and charge 2 of magnitude 2.00 nC , are separated by a distance of 39.0 cm . An electron is released from rest at the point midway between the two charges, and it moves along the line connecting the two charges. What is the speed vfinal of the electron when it is 10.0 cm from charge 1?

Answer 1

As initially everything is at rest, so, the total energy is the potential energy of the configuration. And this is given by
  
  
where, d is the distance between the two stationary charges at the two ends.
And in the 2nd case, let the kinetic energy of the electron is K. And so, the total energy in the final case is
   
  
where, x is the distance of the electron from the charge 1.
And from the energy conservation, we get
  
  
  
   
And for the non-relativistic electron of mass m, the kinetic energy is given by
  
So, we get the final speed as
  
   
Now for the given values,
   
we get the final speed as