Discussion on “the dielectric strength of thin insulating materials” (Farmer), New York, December 12, 1913. (see proceedings for December, 1913)

F. W. Peek, Jr: Three types of insulation are in general use — gaseous, liquid, and solid. The mechanism of breakdown differs in many respects in the three types. Any insulation, under given conditions, ruptures at a given point when the dielectric flux density at that point exceeds some definite value. The total dielectric flux depends upon the capacity and the electromotive force; that is, upon the size and spacing of conductors and the voltage between them. The flux density at various points will also be different, depending upon the configuration of electrode. The flux density at any point is proportional to the gradient at that point. The strength of insulation, therefore, may also be expressed in terms of the gradient measured at the point where rupture occurs. The voltage required to rupture insulation, divided by its thickness, is not a measure of the insulation strength. It is the average gradient. The maximum gradient where rupture starts is much higher. For instance, take two pairs of spheres, one pair a half-centimeter in diameter, spaced one cm. apart, and the other pair two cm. in diameter, spaced one cm. apart. Apply a voltage of 100 kv. across pair No. 1. The gradient is maximum at the surface and is by calculation de/dx = 270 kv./cm. The average gradient e/x = 100/1. On pair No. 2, 100 kilovolts gives de/dx = 135 kv./cm.; e/x = 100 kv./cm. Thus for the same voltage and spacing the actual stress is quite different, depending upon the curvature. If 20-cm. spheres are taken, under the above conditions de/dx = 103 and e/x = 100. Thus with large radius the average gradients and de/dx are approximately equal. This is the reason that in any investigation (other than commercial testing) made to determine the strength of insulation, some electrode is taken in which the dielectric flux density and gradient at various points can be calculated — that is, spheres, parallel wires, or a wire in a cylinder. These may be arranged so that the break is local, as corona in air on two parallel wires at large spacings. The break starts at the surface because the flux density is a maximum there. The conducting corona extends out approximately to a point where the flux density is below the breakdown density. Only when the surfaces are close together does a complete spark-over take place before corona forms.