12(3 Mr. G. F. C. Searle on the 



energy in the field is unaltered by the sudden stopping of the 

 system. 



After a short time the pulse will get clear of the system 

 and then it separates the " old field," which is external to the 

 outer surface of the pulse, from the " new field," which is 

 internal to the inner surface of the pulse. In the old field 

 the electric and magnetic forces are those due to the un- 

 disturbed steady motion of the system, while in the new field 

 the forces are those due to the system at rest. As the pulse 

 advances ^ the energy in the old field continually diminishes 

 to zero, the energy in the new field continually increases to 

 U , and the energy in the pulse tends to the value W. But 

 the energy in the whole field has not been changed by 

 stopping the system, and thus 



U + T = W + U . ..... (13) 



The force required to keep the system at rest does not 

 necessarily vanish directly the velocity of the system has 

 been destroyed, but only after the pulse has got clear of the 

 system. Thus, in the case of a charged sphere of radius a 

 the time 2a/ v will elapse before the pulse gets clear of the 

 sphere. After this time the sphere experiences no force. 



§ 11. When the system is impulsively set into motion at 

 speed u, a force may be required to maintain the speed at the 

 constant value u until the pulse gets clear of the system. As 

 long as the force is necessary, it will do work in causing the 

 charges on the system to move while they are under the 

 influence of the electric forces in the pulse*, and thus the 

 action of the force changes the energy of the electromagnetic 

 field. When a sphere of radius a is set into motion, the time 

 2a/(v — u) will elapse before the pulse gets clear .of the sphere. 

 Alter this time no force is required to keep the velocity of 

 the sphere constant. 



As soon as the pulse has got clear of the system, the energy 

 of the electromagnetic field remains unchanged. In the old 

 field, which is external to the outer surface of the pulse, the 

 electric and magnetic forces are those due to the system at 

 rest. As the pulse advances, the energy in the old field con- 

 tinually diminishes to zero, the energy in the new field 

 continually increases to U + T, and the energy in the pulse 

 tends to AV. Hence, ultimately, the energy in the field has 

 been increased from U to U + T, while W has been lost by 

 radiation. Hence, in setting the system in motion, the force 



* Since H is perpendicular to u, the force on a unit moving charge 

 due to H is fiuli at right angles to u. Hence no work is done in moving 

 the charge while it is under the influence of this force. 



