526 



THE ELECTROMAGNETIC FIELD. [PT. III. CH. XIII. 



in the insulator. Our boundary conditions are then, dividing 

 by , 



(4) 



a -A 



Accordingly we have 



(5) 



1- 



1 + 



2-7TX//, 



2-irXfjb 



Since these two ratios are complex, at the surface of the con- 

 ductor there is a difference of phase between the direct, reflected 

 and transmitted waves. As we increase the conductivity of the 

 conductor the ratio ft'/ft approaches the value 1, in which case 

 the electric force vanishes at the boundary, which is a node for the 

 electric field, while the magnetic field is a maximum. On the 

 other hand, as we increase the frequency of the oscillation or the 

 magnetic inductivity of the conductor the ratio ft'/ft approaches 

 + 1, or the magnetic force vanishes at the boundary, while the 

 electric is a maximum. If we put 



we find for the ratios of the amplitudes of the reflected and trans- 

 mitted to that of the direct waves 



ft' 



ft 



ft 



Accordingly whether r be very great or very small the reflected 

 waves tend to become as great as the direct, while the larger r the 

 less is the magnitude of the transmitted waves. 



