551-555] Kinetic and Potential Energy 483 



the last section by lt <8) 2 , All that remains to be done before we can 



apply Lagrange's equations provisionally (cf. 547) to the interpretation of 

 electromagnetic phenomena is to determine whether the different kinds of 

 energy are to be regarded as kinetic energy or potential energy. 



Kinetic and Potential Energy. 



554. At first sight it might be thought obvious that the energy of 

 electric charges at rest and of magnets at rest ought to be treated as 

 potential energy, wbile that of electric charges or magnets in motion ought 

 to be treated as kinetic. On this view the energy of a steady electric 

 current, being the energy of a series of charges in motion, ought to be 

 regarded as kinetic energy. We have also seen that this energy is to be 

 regarded as being spread throughout the medium surrounding the circuit in 

 which the current flows, and not as concentrated in the circuit itself. Thus 

 we must regard the medium as possessing kinetic energy at every point, the 



t/"2 



amount of this energy being, as we have seen, ~ per unit volume. 



But we have also been led to suppose that the medium is in just the 

 same condition whether the magnetic force is produced by steady currents or 

 by magnetic shells at rest. Thus, on the simple view which we are now 

 considering, we are driven to treat the energy of magnets at rest as kinetic 

 a result which is inconsistent with the simple conceptions from which we 

 started. Having arrived at this contradictory result, there is no justification 

 left for treating electrostatic energy, any more than magnetostatic energy, 

 as potential rather than kinetic. 



555. Abandoning this simple but unsatisfactory hypothesis, let us turn 

 our attention in the first place to the definite discussion of the nature of the 

 energy of a steady electric current. 



Let us suppose that we have two currents i, i f flowing in small circuits at 

 a distance r apart. As a matter of experiment we know that these circuits 

 exert mechanical forces upon one another as if they were magnetic shells of 

 strengths i, i'. Let us suppose that a force R is required to keep them apart, 

 so that initially the circuits attracted one another with a force R, but are 

 now in equilibrium under the action of their mutual attraction and this force 

 R acting in the direction of r increasing. 



If M is the quantity 1 1 dsds', we know that the value of R is 



. ., dM 



R=-^^ -fr (oil), 



this value being found directly from the experimental fact that the circuits 

 attract like their equivalent magnetic shells (cf. 499). 



312 



