This book provides an excellent summary of the fundamental contributions of Faraday and Maxwell. Faraday came from a poor family and was self-taught without much mathematics, but via careful experimentation developed the field concept of electricity and magnetism. Maxwell, an excellent mathematician, presented the fundamental equations of electromagnetism to which Einstein referred in his theory of special relativity.
Maxwell's equations can be expressed using the divergence and curl which are ways of describing how vectors vary in a small region surrounding the point. To visualize curl think of water flowing in a river. The vector here is the speed and direction of the flow. Imagine a tiny paddle wheel somehow fixed at a point in the river but with its axis free to take up any angle. If and only if the water is flowing faster on one side of the paddle wheel than the other, the wheel will spin, and its axis will take up the position that makes it spin fastest. The curl of the water flow at out point is a vector whose magnitude is proportional to the rate of spin, and whose direction is along the axis of spin. At a point in empty the curl of the electric field force at a oint is proportional to the rate at which the magnetic field force there is changing, and vice versa.
Divergence or div is a scalar. The divergence of the water flow at or fixed point is a measure of the excess of water flowing out of a small region surrounding the point compared with that flowing in. At a point in empty space the divergence of the electric field force and the divergence of the magnetic field force are both zero.
