Coulomb Potential

The Coulomb potential describes the potential felt by two charged particles: particles with the same electric charge repel each other, while particles of opposite charge attract each other.

Electric Charge

positive

negative

Mass

∞

The Coulomb potential between a particle of charge $q_1$ and a particle of charge $q_2$ at distance $r$ from each other is given by

V = - \frac{1}{4\pi} \frac{q_1q_2}{r} \; .

This potential gives rise to a force $\vec F = - \nabla V$ , which is used in Newton’s equation of motion

m \frac{d^2\vec{x}}{dt^2} = \vec F \; ,

to simulate the trajectory of the particles. To keep the simulation stable, a soft core repulsion is added to the potential and prevents the particles from overlapping.