How to connect maxwells theory of electromagnetism and mechanical model(newtonion physics)of atom ?
You mean like the Bohr model?? He postulated that an electron orbited the nucleus just like a planet orbits the sun. Instead of gravity, though, the centripetal force is provided by electrostatic attraction. Note that this isn’t a great model–Maxwell’s equations predict that an orbiting electron will radiate away its energy, so Bohr had to postulate that this just wouldn’t happen. Also, classical mechanics doesn’t apply to physics on an atomic scale–you need quantum mechanics for an accurate description.
