Question

An electron and a positron are located 17 m away from each other and held fixed by some mechanism. The positron has the same mass and the same magnitude of charge as those of the electron, but its charge is positive. The electron and the positron are released at the same time by the mechanism. The electron and the positron begin to speed up towards each other. What velocities should they have when they are 1.3 m away from each other?

Answer 1

Using energy conservation:

KEi + EPEi = KEf + EPEf

KEi = Initial kinetic energy of positron-electron system = 0 J, since intially both particle were at rest

EPEi = initial electric potential energy of system = k*q1*q2/ri

EPEf = final electric potential energy of system = k*q1*q2/rf

KEf = final KE of system = (1/2)*m1*V^2 + (1/2)*m2*V^2

Since given both particle have same mass and charge, So force of attraction between both charge will be same, So both particle will be moving with same speed

m1 = m2 = mass of electron/positron = 9.1*10^-31 kg

q1 = charge on electron = -e = -1.6*10^-19 C

q2 = charge on positron = +e = +1.6*10^-19 C

ri = Initial distance between electron-positron = 17 m

rf = final distance between electron-positron = 1.3 m

So Using given values:

0 + k*q1*q2/ri = (1/2)*m*V^2 + (1/2)*m*V^2 + k*q1*q2/rf

m*V^2 = k*q1*q2*(1/ri - 1/rf)

V = sqrt ((k*q1*q2/m)*(1/ri - 1/rf))

V = sqrt [(9*10^9*1.6*10^-19*(-1.6*10^-19)/(9.1*10^-31))*(1/17 - 1/1.3)]

V = 13.41 m/s = final speed of both particles

Let me know if you've any query.