172 ADVANCED ELECTRICITY AND MAGNETISM. 



+ Q coulombs per centimeter of length, and the inner surface 

 of the outer cylinder carries Q coulombs per centimeter of 

 length; and these charges are spread uniformly around the 

 cylinders because of the complete symmetry. The two cylinders 

 constitute a condenser, and therefore : 



Q = CE (i) 



where Q is the charge per unit length (positive on one cylinder, 

 negative on the other), C is the capacity per unit length, and E 

 is the electromotive force or potential difference between the 

 cylinders. If we can calculate E for a given value of Q, this 

 equation will give us an expression for C. 



The electric field intensity e in volts per centimeter at the 

 point p in Fig. 114 is: 



BQ i 

 $==.- (2) 



27T X 



according to Art. 94, where x is the distance of p from the 

 axis in centimeters. Multiplying the value of e in volts per 

 centimeter by A# centimeters we get the electromotive force 

 along Ax in volts, that is, AE = e-Ax, or: 



so that: 



BQ 



But C = -~ according to equation (i). Therefore, from equa- 

 H, 



tion (4), we get: 



where C is the capacity in farads of each centimeter of length 

 of the coaxial cylinders, and B is 1.131 X io 13 . 



Equation (5) refers to coaxial cylinders with air between. 



