Mechanics and Maxwell's Equations
Thomas A. Garrity · Cambridge University Press eBooks · 2015
: Despite linking the electric and magnetic fields, Maxwell's equations are worthless for science if they do not lead to experimental predictions. We want to set up a formalism that allows us to make measurements. This chapter will first give an overview of Newtonian mechanics. Then we will see how the electric and magnetic fields fit into Newtonian mechanics. In the final section, we will see that the force from the electric field (Coulomb's law), together with the Special Theory of Relativity and the assumption of charge conservation, leads to magnetism. Newton's Three Laws The development of Newtonian mechanics is one of the highlights of humanity. Its importance to science, general culture, and our current technological world cannot be overstated. With three laws, coupled with the calculational power of calculus, much of our day-to-day world can be described. Newton, with his laws, could describe both the motions of the planets and the flight of a ball. The world suddenly became much more manageable. Newton's approach became the model for all of learning. In the 1700s and 1800s, bright young people, at least in Europe, wanted to become the Newtons of their fields by finding analogs of Newton's three laws. No one managed to become, though, the Newton of sociology. We will state Newton's three laws and then discuss their meaning. We quote the three laws from Halliday and Resnick's Physics [32]. Newton's First Law: Every body persists in its state of rest or of uniform motion in a straight line unless it is compelled to change that state by forces impressed on it. (On page 75 in [32], quoting in turn Newton himself.) Newton's Second Law: Force = mass · acceleration. Newton's Third Law: To every action there is always an opposed equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.