Multilayer Coils with Square and Circular Section. 967 



Now the average electric intensity over AB depends on 

 the rate at which the average potential changes in the 

 direction normal to AB in the neighbourhood of AB. If, 

 then, the distance of AB from an arbitrary line parallel 



Fig-. 4. — Inside structure of multilayer coil. 



to AB is y, then the average electric displacement over AB 

 in the direction of y increasing may be written as 



47rlO n x -8-989 dy ' 



where V is the average potential, and K e is a constant which 

 depends on the relative values of the radius and the distances 

 between two adjacent layers as well as wires in the same layer, 

 and also on the specific inductive capacity of the medium 

 between the wires. (8'989 is the square of 2'9982.) The 

 constant K e may be called the effective dielectric constant of 

 the composite dielectric formed by the wires and the medium 

 between the wires. In what follows, K e is set equal to 

 8-989 xl0 ll K e . 



Let BC = Ay. 



Then the flux out through DC is 



4-7T \dy )y+ly 



Therefore the flux of the electric displacement out through 

 the surface of the prism is . 



* C .AB 



RdV\ (dV\l K e d 2 Y . r^r 



4tt L\dy ? y+Ay \dy 

 if Ay is small. But AB . Ay is the volume of the prism. 



