Physics 230 February 22

We are to investigate a system of three charges lined up as shown in the diagram.
 
 


 
 

The system contains three distinct pairs of charges, two pairs with charges + and - q and separation d and one pair with equal charges q and separation 2d. Thus the energy is:

The energy is negative, and so the system collapses. Since the forces all act along the same line, and the force on each of the outer charges has the same magnitude (but opposite direction), the system maintains its shape as it collapses. In the "before" state the separation is d0 while in the after state it is d0/2.
  Before After
PE -3kq2/2d0 -3kq2/d0
KE 0 2(mv2/2)= mv2
Total -3kq2/2d0 mv2-3kq2/d0

 

Setting the totals equal, we find: