Let's say I have two positive charges approaching one another at the same speed with only their mutual forces acting on one another. Total momentum (= 0) and energy is conserved and the charges eventually move away from one another at the same velocity.
Now suppose an external force acts on one of the charges to keep it stationary while the other one is free to move as before. Even though energy is still conserved, the total momentum only comes from one of the charges, and therefore isn't balanced by an equal and opposite momentum from the other charge to keep the total momentum zero:
What is it about momentum and energy that allows a stationary force to affect the conservation of one, but not the other?