CHAPTER XVII. 



DISPLACEMENT CCBREXTS. 



GENERAL EQUATIONS. 



569. OUE development of the theory of electromagnetism has been based 

 upon the experimental fact that the work done in taking a unit magnetic 

 pole round any closed path in the field is equal to 4rv times the aggregate 

 current enclosed by this path. But it has already been seen ( 534) that this 

 development of the theory is not sufficiently general to take account of 

 phenomena in which the flow of current is not steady: "the aggregate current 

 enclosed by a path" is an expression which has a definite meaning only when 

 the flow of current is steady. Before proceeding to a more general theory, 

 which is to cover all possible cases of current flow, it is necessary to deter- 

 mine in what way the experimental basis is to be generalised, in order to 

 provide material for the construction of a more complete theory. 



The answer to this question has been provided by Maxwell According 

 to Maxwell's displacement theory ( 171), the motion of electric charges is 

 accompanied by a i displacement " of the surrounding medium. The matin 

 produced by this displacement will be spoken of as a " displacement-current,'' 

 and we have seen that the total flow which is obtained by compounding the 

 displacement-current with the current produced by the motion of electric 

 charges (which will be called the amdwctitm-cmi i gal), will be such that the 

 total flow into any closed surface is, under all circumstances, zero. Thus if 

 are any two surfaces bounded by the same closed 



path s, the total flow of current across S^ is the same as ^___ ^i__^^ 



the total flow, in the same direction, across &, so that ^ -^ > * 



either may be taken to be the flow through the circuit 

 t, Maxwefffl theory proceeds on the supposition that 



in any flow of current, the work done in taking a unit magnetic pole round * 

 lal to the total flow of current, including the displacement-current, 

 through s. The justification for this supposition is obtained as soon as it is 

 seen how it brings about a complete agreement between electromagnetic 

 theory and innumerable facts of observation. 



570. Let us first put the hypothesis of the existence of displacement- 

 currents into mathematical language. Let , r, tr be the components of the 



