Assuming that the charges are moving nonrelativistically (v≪c), what can you say about the relationship between the magnitudes of the magnetic and electrostatic forces?\

Assuming that the charges are moving non-relativistically, this means that the velocity is very small as compared to the speed of light. But still moving at this speed they radiate a substantial amount of energy that remains conserved. Although the Kinetic and Potential energy interchange but the overall internal energy remains constant. The magnitude of magnetic and electrostatic forces change according to the change in speed of moving charges.