Abstract :
The algebra of the integral potential (pot) operator, in combination with the usual differential operators, is briefly discussed. The main algebraic results are simple, easily remembered and of interest in themselves. A particularly important result is the operational equation that shows the separation of any vector field into two unique partial fields, one having zero curl and the other zero divergence. The algebra is applied in the transformation of the well known differential electromagnetic equations into various integral equations, in terms of the total (applied and induced) sources of the field. The transformation process is usually based on the equation of separation mentioned above. It is simple, and its routine nature leaves the mind largely free to concentrate on the physical interpretation of the results. Only quasi-static fields are discussed. It is well known that the concept of sources does not fail in a more general time-varying field, and it is intended to extend the application of pot algebra in this direction in later work. A novel form of infinite operational series is presented, which expresses the total magnetic field explicitly in terms of the inducing field, in a region of varying permeability. The series is known to be convergent in particular cases, but work is still proceeding on a general proof of convergence. The use of pot algebra stresses the close relation between equations that emphasize the field structure of an electromagnetic system and equations that emphasize the corresponding source structure. The ability to visualize the system in both ways is a valuable aid to clear understanding.
