Vector Differential Equations in Coulomb's Field Calculations

[abluphoton]

Homework Statement

hi all... i was assigned in my class to do some basic coulomb's field calculation. considering 4 source charges calculating there resultant field anywhere in the space around them. i was able to do that... but later i tried to extend it by giving up the assumption that the source charges are fixed.

i considered 2 point charges and tried to calculate field around them with themselves in motion. i did it fairly well. until i got stuck at a point that seemed like a vector differential equation. will be glad if someone helps me out with this. thanks in advance.

Homework Equations

(|S|)*(s") = [constant vector]

(|S|) here is the magnitude of the position vector and (s") will be acceleration a vector.

The Attempt at a Solution

i haven been taught must about this kind of mathematics. I am now looking for an equation of 'S'

 

[abluphoton]

im still waiting :(