# Monster E&M Question (Coulomb's Law, Electric Potential, Kinematics)

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## Homework Statement

A proton (charge +1e and mass 1.67e-27kg) and an alpha particle (charge +2e and mass 6.64e-27kg) are placed 3 fm (1 fm=10e-15m) apart.
a)what is the force on each particle
B)what is the potential energy of the system?
c)what is the acceleration of each particle at the beginning?
d)after a long time the two particles are far apart. what is the speed of each particle at this point?

## Homework Equations

$F = ( q_1 q_2) / 4 π ε_0 r^2 = (k q_1 q_2) / r^2$
$U = q v = ( q_1 q_2) / 4 π ε_0 r$
$K E = 1 / 2 m v^2$
$F = E q = m a$

## The Attempt at a Solution

a) Using Coulomb's Law, I found the force to be 51.2 N.
b) substituting my values into the second equation above, I got that the potential energy of the system is 1.5e-13 J.
c)Using the fourth equation above I found the accelerations. For the proton I got 3e28 m/s^2. For the alpha particle I got 8e27 m/s^2.
d) This part got a little tough. Realizing that the acceleration decreases as the particles move apart, I tried to integrate their acceleration from their initial separation out to infinity, but this quickly proved to be tedious/confusing. Looking at it again, I realized that as the particles move towards infinity all of the potential energy will be converted into kinetic energy. So I solved equation 3, substituting my answer from b) in for the kinetic energy and the mass of each particle. I found the velocity of the proton to be 1.34e7 m/s and the velocity for the alpha particle to be 6.72e6 m/s.

Did I do this correctly? This question is from an old test my prof gave us to study (I don't have the solution) and I have no intuition for how quickly these types of particles should be moving.

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Yes.The procedure you did is correct.

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Thanks! If I wanted to continue on my initial path of integrating (no pun intended) the acceleration to get the final velocity, could somebody show how that would work?

What the supposed pun supposed to be?

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path of integrating = path integral. not a good one, but gimme a break -- I've been studying all day.