C.8.6 Geometric considerations

Internal charging can be most easily calculated by considering a 1-d planar structure. However, even in this simple case, the conductivity varies across the material due to the changing electric field and radiation induced conductivities. The electric field varies across the dielectric and the maximum electric field in the equilibrium state is found at the boundary between the dielectric and the underlying conductor.

Cable insulators usually exhibit cylindrical symmetry. For a cable with a single central conductor, the cylindrical shape leads to a concentration of current as it flows to the centre. This increases the electric field over the equivalent planar case.

For insulators with a complicated 3-d structure, calculation of the maximum electric field requires both a 3-d model of the charge deposition and a 3-d model of the currents and electric fields. However, even in this case, the maximum electric field is likely to occur at a dielectric/conductor boundary.