RC time constant

You introduced 1 Coulomb worth of electrons into the inner volume of a dielectric material with ϵr=6. 30 minutes later, you found that only 36.79% of the electrons were in the inner volume. Determine the conductivity σ of the dielectric material.

Correct result:

s =  2.95E-14 S/m

Solution:

Q=1 C ε=6 ε0=8.85 10128.851012 F/m t=30 min s=30 60  s=1800 s p=36.79 % T=t=1800=1800 s   T=R C  C=ε ε0 S/d=ε K T=R ε ε0 S/d R=ρ d/S  T=ρ d/S ε ε0 S/d T=ρ ε ε0  ρ=T/(ε ε0)=1800/(6 8.851012)=33898305084746 Ω     s=1/ρ=1/33898305084746=2.951014 S/m



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