18 BELL SYSTEM TECHNICAL JOURNAL 



Electromagnetic Theory 



There is a further gap which it is to be hoped can in the future be 

 bridged for those students who are sufficiently advanced to become 

 famihar with the general electromagnetic theory. To what extent it is 

 practical to teach general electromagnetic theory to undergraduates 

 is a question which is perhaps beyond the scope of this paper. How- 

 ever, those five differential equations as formulated by Maxwell and 

 Lorentz which form the general mathematical statement of the funda- 

 mental discoveries of Ampere, Faraday and the other pioneers of 

 electric science are the Magna Charta of electric science of today, and 

 with the rapid development of the electrical arts in various directions 

 constant recourse must be had to these fundamental equations for the 

 establishment of correct electrical principles. 



The simplified electric circuit theory which we have just discussed, 

 which may be called the classic theory, serves very well for the great 

 bulk of problems of electrical transmission of today. However, already 

 there are situations both in the power transmission art and in the com- 

 munication art in which the approximations which these equations 

 involve are not valid, and for the solution of practical cases recourse 

 must be had to the more general equations. These practical cases 

 include the distribution of current in the earth when one side of a 

 circuit is grounded, the inductive effects produced in other electrical 

 circuits from a grounded circuit, and the transmission characteristics 

 of submarine cables in which the sea water forms a part of the return 

 path. 



The classic circuit theory expresses the electrical quantities in terms 

 of the total currents flowing in conductors and the voltages between 

 these conductors, and expresses the aggregate energies in terms of 

 inductances and capacities, and the dissipation in terms of resistances. 

 The general equations of the electromagnetic theory express the electric 

 quantities in terms of elementary current and charge densities, and the 

 electric and magnetic fields are expressed in terms of field strengths. 

 These, then, are the rigorous equations in differential form. In the 

 classic theory the current and charge densities and field strengths are 

 integrated into more easily manipulated totals. In other words, the 

 electric circuit theory deals with macroscopic or large scale phenomena 

 and the electromagnetic theory deals with microscopic or small scale 

 phenomena. 



What are the approximations involved in the classic theory and what 

 conditions must be met for these to be good approximations? This 

 matter has been treated in a very interesting way in some recent 

 papers by Mr. John R. Carson. In brief, Mr. Carson's papers point 



