For example if two charged particles attract each other due to electrostatic forces, the internal force on them is opposite but so is their displacement.
So work done on them doesn't cancel out, but instead adds.
So does that mean that work done on the system by the internal force is non-zero?
Each charge does the same amount of positive work on the other. That means each charge transfers the same amount of energy to the other charge for a net energy transfer (net work) between the charges of zero. The result is there is no displacement of the center of mass of the two particle system, which is consistent with the fact that the net work done on the system is zero.
Moreover, the increase in kinetic energy of the system equals the decrease in electrical potential energy of the system due to the charges moving towards one another.
Hope this helps.
When characterizing a force as “internal” or “external” you need to be very clear what is the system. In your example you have two charges, but you also have the electromagnetic field.
If you consider the system to be only the charges themselves then the forces from the EM field are external, not internal. In this case the field does work on each charge, and the work done by the external forces on the system is non-zero.
If you consider the system to be the charges together with the associated EM field, then the forces are internal forces. No work is done on the system by the internal forces, but a non-zero amount of the system’s internal EM energy is changed to internal mechanical energy.
Paying attention to the choice of your system is critical
