213-215] Images 187 



Thus the surface density varies inversely as SQ\ so that it is greatest at 

 C and falls off continually as we recede from the radius 0(7. The total 



PCI 



charge on the sphere is -= , as can be seen at once by considering that the 



total strength of the lines of force which end on it is just the same as would 

 be the total strength of the lines ending on the image at R if the conductor 

 were not present. 



FIG. 62. 



Figure 62 shews the lines of force when the strength of the image is a 

 quarter of that of the original charge, so that /= 4a. It is obtained from 

 fig. 19 by replacing the spherical equipotential by a conductor, and annihi- 

 lating the field inside. 



Superposition of Fields. 



215. We have seen that by adding the potentials of two separate fields 

 at every point, we obtain the potential produced by charges equal to the total 

 charges in the two fields. In this way we can arrive at the field produced 

 by any number of point charges and uninsulated conductors of the kind we 

 have described. The potential of each conductor is zero in the final solution 

 because it is zero for each separate field. 



There is also another type of field which may be added to that 

 obtained by the method of images, namely the field produced by raising the 

 conductor or conductors to given potentials, without other charges being 

 present. By superposing a field of this kind we can find the effect of point 

 charges when the conductors are at any potential. 



