A charge Q is fixed in place A charge q of mass m1 is releas

A charge Q is fixed in place. A charge q of mass m1 is released from rest a distance d from Q. Determine the velocity of q as a function of its distance x from Q. (Yes, you solved this on the electrostatics assignment but this time use energy techniques.) b: Redo part a but this time charge Q (of mass m2) is free to move as well.

Solution

force, F= m1*a and    F = k*Q*q/x^2

m1*v*dv/dx = k*Q*q/x^2

integrating on both sides, we get

(m1*v^2)/2 = -k*Q*q/x + c

apply, v=0 then x=d, so c = k*Q*q/d

thus, the speed is,

         v^2 = 2/m1*(k*Q*q(1/d - 1/x))

         v= [2/m1*(k*Q*q(1/d - 1/x))]^1/2