89-92] Mechanical Force 79 



Submarine Cables. 



91. Unfortunately for practical electricians, a submarine cable forms 

 a condenser, of which the capacity is frequently very considerable. The 

 effect of this upon the transmission of signals will be discussed later. A cable 

 consists generally of a core of strands of copper wire surrounded by a layer of 

 insulating material, the whole being enclosed in a sheathing of iron wire. 

 This arrangement acts as a condenser of the type of the coaxal cylinders 

 investigated in 82, the core forming the inner cylinder whilst the iron 

 sheathing and the sea outside form the outer cylinder. 



In the capacity formula obtained in 82, namely 



K 



let us suppose that a = ^ cm., 6=1 cm. and that ^T = 3'2, this being about 

 the value for the insulating material generally used. Using the value 

 logg 2 = '6931 5, we find a capacity of 2'31 electrostatic units per unit length. 

 Thus a cable 2000 miles in length has a capacity equal to that of a sphere of 

 radius 2000 x 2'31 miles, i.e., of a sphere greater than the earth. In practical 

 units, the capacity of such a cable would be about 827 microfarads. 



MECHANICAL FORCE ON A CONDUCTING SURFACE. 



92. Let Q be any point on the surface of a conductor, and let the 

 surface-density at the point Q be cr. Let us draw any small area dS 



FIG. 36. 



enclosing Q. By taking dS sufficiently small, we may regard the area as 

 perfectly plane, and the charge on the area will be o-dS. The electricity on 

 the remainder of the conductor will exert forces of attraction or repulsion on 

 the charge vdS, and these forces will shew themselves as a mechanical force 

 acting on the element of area dS of the conductor. We require to find the 

 amount of this mechanical force. 



