Somewhat late, but my postings have been bouncing due to an addressing
problem.
1. If you wish to consider the time delay in pushing an object with a
long rod, then you must give up the rigid body approximation. A rigid body
has a zero delay in propagating forces (ie infinite velocity of propagation
of sound, etc.) THe rod must be considered in sections, with each one reacting
in accord with Newton's Laws w. respect to the neighboring sections.
The resulting internal motions conserve momentum and energy during the
period before the far end begins to affect the load.
2. The Electromagnetic field can carry momentum and energy as well as
exert forces (radiation reaction) on the sources of changes of the fields.
The effect of one charge on another is therefor a situation involving
three 'objects' with interactions between charges and field occuring at
different times.