Question

The relaxation time of mica with σ= 10˄-15 s/m and εr=​6

Answer 1

Explanation:

In a region that has uniform conductivity and permittivity, charge conservation and Gauss' law determine the unpaired charge density throughout the volume of the material, without regard for the boundary conditions. To see this, Ohm's law (7.1.7) is substituted for the current density in the charge conservation law, (7.0.3),

equation GIF #7.78

and Gauss' law (6.2.15) is written using the linear polarization constitutive law, (6.4.3).

equation GIF #7.79

In a region where and are uniform, these parameters can be pulled outside the divergence operators in these equations. Substitution of div E found from (2) into (1) then gives the charge relaxation equation for u.

boxed equation GIF #7.17

Note that it has not been assumed that E is irrotational, so the unpaired charge obeys this equation whether the fields are EQS or not.

The solution to (3) takes on the same appearance as if it were an ordinary differential equation, say predicting the voltage of an RC circuit.

Answer 2

Given:

σ=$10^{-15}$ S/m

Εr=6

To find:

relaxation time

Solution:

Relaxation time is the time taken for a system to return to its equilibrium state.

$t_r$=(ΕoΕr)/σ

Putting the value in the above equation, we get,

$t_r$=(8.85×$10^{-12}$×6)/($10^{-15}$×60×60)

Evaluating the above equation, we get the value as follow,

⇒$t_r=$15

Therefore, the relaxation time under the given conditions is 15 hours.