The equation J sigmaE defines the conductivity sigma of a m

The equation J = sigmaE defines the conductivity, sigma, of a material, i. Explain what the quantities J and E represent complete with units. What are the consequences of Eqn. 1 for a perfect dielectric, and a perfect conductor. Given that the resistance of a resistor of an arbitrary shape is show that the conductance per unit length of a coaxial cable with an insulation conductivity, sigma, is G\' = g/l = 2pisigma/in (b/a) where a is the inner radius and b is the outer radius of the coax cable.

Solution

(i)    Current density of a material is given by

                     J= E

where E is the electric field and is the electrical conductivity.

Conductivity is the reciprocal (inverse) of electrical resistivity and has the SI units of siemens per metre (S m¹), and E has the SI units of newtons per coulomb (N C¹) or, equivalently, volts per metre (V m¹).

(ii)     A perfect conductor cannot contain an electrostatic field within it. So E=0.

if E=0 then Current density(J) value becomes zero.

So for a perfect conductor Current density J=0