TABLE OF CONTENTS In this chapter, we shall make a detailed investigation of the electric fields generated by stationary charge distributions using Maxwell's equations. In particular, we shall examine the interaction of electrostatic fields with ohmic conductors.
Consider a collection of N static point charges q i located at position vectors r i, respectively (where i runs from 1 to N). What is the electrostatic energy stored in such a collection? In other words, how much work would we have to do in order to assemble the charges, starting from an initial state in which they are all at rest and very widely separated?
Well, we know that a static electric field is conservative, and can consequently be written in terms of a scalar potential:
We also know that the electric force on a charge q located at position r is written
The work we would have to do against electrical forces in order to slowly move the charge from point P to point Q is simply
The negative sign in the above expression comes about because we would have to exert a force -f on the charge, in order to counteract the force exerted by the electric field. Recall, finally, that the scalar potential field generated by a point charge q located at position r ? is
Let us build up our collection of charges one by one. It takes no work to bring the first charge from infinity, since...
