140 Mr. E. A. Biedermann on the 



I wish to express my best thanks to Sir Ernest Rutherford 

 for his kind permission to carry out this research in his 

 laboratory, and for giving me many suggestions during the 

 course of the investigation. My thanks are also due to 

 Mr. Ttmstall and Mr. Kay for their kind assistance. 



The Physical Laboratory, 

 Victoria University of Manchester, 

 November 191(1 



IX. The Energy in the Electromagnetic Field. 

 By E. A. Biedermann, B.Sc, AM.l.E.E* 



^^HE object of the present paper is to point out certain 

 jl consequences of the assumption that the magnetic 

 or kinetic energy density in an electromagnetic field is 

 represented by H 2 /8tt, and to suggest a possible modifica- 

 tion of this expression. The calculation on the above basis, 

 of the kinetic energy in the field due to any system of 

 spherical charges, either surface or volume, may be effected 

 by elementary methods, as has been shown recently by 

 Prof. Anderson f for the case of point charges, and earlier 

 by Prof. Nicholson % for two or more point charges in the 

 same straight line. Whilst the derivation of the expression 

 for the energy for the somewhat more general case of 

 spherical charges of finite size is not the object of this 

 paper, yet the calculation will be shortly outlined for the 

 sake of completeness, and because certain integrals occurring 

 will be required later. 



The energy of a system of charges follows at once from 

 that of a pair by means of the relation 



H 2 = SK 2 + /3 r 2 + 7; 2 ) + 2SX(a r « s 4-^/3 tf H- 7r7s ), . (1) 



( a r > &, 7 r ) 5 (* s > &> %)•> &c *' denotm g tne components of 

 magnetic force at a point due to charges e r , e s , &c, respec- 

 tively. The individual energy of any one of the charges e r 

 of the system (i. e., the energy associated with that charge 

 when the rest of the system is removed) is, for a spherical 



* Communicated by the Author. 



+ Prof. A. Anderson. Phil. Mag. Aug. 1916. 



t Prof. Nicholson, Proceedings of the Physical Society, April 1915. 



