ii8 
PHYSICS: L. PAGE 
Proc. N. a. S. 
right. Then the rate of change of the electric intensity at P due to the 
formation of new Hnes is 
(c — v)V-E. 
Adding this to the expression for E obtained above, and using Coulomb's 
law to eliminate V-E, it is seen that 
V X (c X E) = E + pv. 
The magnetic intensity H is defined by 
H ^ - c X E. 
c 
Therefore 
V X H = - (E + pv). (2) 
c 
This is Ampere's law for the field due to a single charged particle. As 
it is linear in E and H, the same law holds for the resultant of the simple 
fields due to any number of charged particles. 
Next consider a charged particle e (fig. 3) at rest relative to the observer 
Fig. 3 
but having an acceleration / to the left. Let eP be the path of a moving 
element emitted from the charge at the time zero, and eA that of a moving 
element belonging to the same line of force, but emitted at the time dt. 
As the velocity of the charge has changed in this time, these paths will 
make different angles with the acceleration. The line of force at P at 
time r/c will have the direction of ^P, or p. Evidently 
r = c/, 
ii = — cdt + tdc, 
Y 
p = zdt — - Jc, 
c 
and the electric intensity at P at the time rjc is given by 
E = ^ P 
^'kt'' pcosQPH 
e j r ) 
