CHAP, iv.] ELECTRICITY AND MAGNETISM. 205 



250. Electric Images. It can be shown mathe- 

 matically that if + q units of electricity are placed at a 

 point near a non-electrified conducting sphere of radius 

 r, at a distance d from its centre, the negative induced 



charge will be equal to - r ~ d q, and will be distributed over 



the nearest part of the surface of the sphere with a 

 surface-density inversely proportional to the cube of the 

 distance from that point. Sir W. Thomson pointed out 

 that, so far as all external points are concerned, the 

 potential due to this peculiar distribution on the surface 

 would be exactly the same as if this negative charge were 



r 2 

 all collected at an internal point at a distance of -\ behind 



the surface. Such a point may be regarded as a virtual 

 image of the external point, in the same way as in optics 

 we reeard certain points behind mirrors as the virtual 

 images of the external points from which the rays pro- 

 ceed. Clerk Maxwell has given the following defini- 

 tion of an Electric Image : An electric image is an 

 electrified point, or system of points, on one side of a surface, 

 which would produce on the other side of that surface the 

 same electrical action which the actual electrification of 

 that surface really does produce. A charge of + elec- 

 tricity placed one inch from a flat metallic plate induces 

 on it a negative charge distributed over the neighbouring 

 region of the plate (with a density varying inversely as 

 the cube of the distance from the point) ; but the 

 electrical action of this distribution would be precisely 

 represented by its " image," namely, by an equal quantity 

 of negative electricity placed at a point one inch behind 

 the plate. Many beautiful mathematical applications of 

 this method have been made, enabling the distribution 

 to be calculated in difficult cases, as, for example, the 

 distribution of the charge on the inner surface of a hollow 

 bowl. 



251. Electric Force exerted by a Charged 



TK > 



uar ?* 





