Electrostatics : Coaxial cable with two dielectrics

Problem statement

Consider a coaxial cable filled with two dielectrics. To fulfill the objective it is necessary to calculate the electric field as a function of radius between the conductors. Applying Gauss' law gives two different expressions for the value of E, the electric field strength.

Objective : to find the capacitance per unit length C between the conductors.
Principles : Gauss' law.

Method of analysis :	1) define the potential difference V between the conductors,
			2) define the magnitude of the charge per unit length [rho] on the conductors.

Sketch :

Maths :

Matlab(R) solution
Solution variables
Input variables


Charge per unit length, q (coulombs/metre)		
Radius of inner conductor, a (metres)			
Radius of outer conductor, b (metres)			
Radius of dielectric boundary, c (metres)		
Radius from centre, r (metres)				
Relative permittivity of the inner dielectric, er1 	
Relative permittivity of the outer dielectric, er2 	



Output variables


Electric field strength E in inner region
Electric field strength E in outer region
Potential difference between the conductors, V
Capacitance per unit length , C