Question

I want you to solve the below statement that about Electric field and dielectric refraction.

The question is to Explain the behavior of electric field in the interface of two insulation materials of different relative permittivity.

Answer 1

The electric field stress is inversly proportional to the permittivities of dielectrics and the inner radii of the dielectrics.

Capacitance Grading or Dielectric Grading

In this type of grading, the homogeneous dielectric is replaced by layers of dielectric having a different value of relative permittivity. For getting a uniform stress, an infinite number of dielectric will be required. The electrical stress can be uniformly distributed by using two or more dielectric having suitable permittivity.

The dielectric stress is given by the equation

Let us considered a cable having three dielectrics of relative permittivity ?1, ?2, and ?3, such that ?1< ?2< ?3. Let r1, r2 and R be the outer radii of the dielectric.

The potential difference across the inner layer is

Similarly the potential difference between r1 and r2 i.e., across the middle layer

and the potential difference between r2 and R i.e., across the outer layer

The total potential difference between core and earthed sheath

The capacitance of the cable

The maximum stress is given by

In case the maximum stress is the same in the each layer

The total voltage applied across the cable

gmax represent the peak value of electrical stress, and all the voltages are represented in peak values, not in RMS value.