CHAPTER VIII. 



METHODS FOR THE SOLUTION OF SPECIAL PROBLEMS. 



THE METHOD OF IMAGES. 



Charge induced on an infinite uninsulated plane. 



208. THE potential at P of charges e at a point A and e at another 

 point A is 



F =^p-^p < m >- 



and this vanishes if P is on the plane which bisects AA at right angles. 

 Call this plane the plane 8. Then the above value of V gives F= over 

 the plane $, F=0 at infinity, and satisfies Laplace's equation in the region 

 to the right of $, except at the point A, at which it gives a point charge e. 



FIG. 57. 



These conditions, however, are exactly those which would have to be satisfied 

 by the potential on the right of if were a conducting plane at zero 

 potential under the influence of a charge e at A. These conditions amount 

 to a knowledge of the value of the potential at every point on the boundary 

 of a certain region namely, that to the right of the plane 8 and of the 

 charges inside this region. There is, as we know, only one value of the 



