THE FORCE ON A SMALL CHARGED BODY 67 



some modifications suggested by the experiments which we have 

 described. 



Definition of electric intensity. If a small positively 

 charged body be placed at any point in a field, the body and 

 its charge both being so small as not to affect the previous 

 charges sensibly, the force on the body per unit charge is termed 

 the electric intensity at the point. We shall usually denote the 

 intensity bv E. 



Definition of the unit quantity. If two small bodies 

 charged with equal quantities and placed 1 cm. apart act each on 

 the other with unit force of 1 dyne, each is said to have unit 

 charge on it. Then unit charge produces unit intensity at unit 

 distance. At distance d a quantity Q has intensity Q/d 2 . If 

 at the point we place a body Ganged with Q', the force on the body 

 is W/ffl. 



Relation between electric intensity and electric 

 Strain. It' a small quantity of electricity Q is placed at a point 

 the values of the electric strain D and of the electric intensity E at 

 a distance d from it are given by 



Whence E = 4?rD. 



Tlii> n l.ition ho Id ing for each element of the electrification to which 



irld is due, it must hold for tin- resultant of all the elements. 



I > to be noted that it is only true when the medium is air, for 



then i^ the intensity Q/cP for each element. As a particular 



case we have another proof of the proposition already proved in 



Chapt. i III. \i/. : 



The intensity just outside the surface of a con- 

 ductor is 4?r x surface density. Tor the strain is by defini- 

 tion measured by a-. Hence the inten>itv N ITTO-. 



Lines and" tubes of force. The lines and tubes of strain 

 may also be regarded in inn-crv>talline media as lines and tubes of 

 force or inteiiMty, and the various strain properties of such tubes 

 may be stated in terms of intensity. The most important of 

 /. that area x strain is constant and equal to unity along a 

 unit tube, becomes: area of cross-section X intensity = 4?7r along 

 a unit tube. The relation between strain and intensity is not to 

 be regarded merely as a numerical definition of one in terms of the 

 other. It expresses a phyncftl f ct, viz. that whichever method we 

 adopt to explore the field, the force on a small electrified body or 

 the charge gathering on one side of a properly held proof plane, 

 the field varies in the same proportion from point to point by either 



