Permittivity values in conductors

[ksnf3000]

Hello All,

I am a masters student in electronics engg and reading technical electrodynamics. Please let me know when the electric current density becomes more than the displacement current (for a conductor ) why is the value of ε≈-jσ/ω

Quick replies will be highly appreciated!

Thanks and Regards,

ksnf3000

 

[Hassan2]

Hello All,

I am a masters student in electronics engg and reading technical electrodynamics. Please let me know when the electric current density becomes more than the displacement current (for a conductor ) why is the value of ε≈-jσ/ω

Quick replies will be highly appreciated!

Thanks and Regards,

ksnf3000

High ksnf3000,

electric current density :

$J=σE$

displacement current density :

$J_{d}=\frac{\partial D}{\partial t}$

for a steady stead sinusoidal field,

$J_{d}=jωD=jωεE$

the ratio is $\frac{ωε}{σ}$

when $ωε=σ$, the magnitudes become the same. Considering typical values of the parameters, this happen at very high frequencies.

I hope that helps.

 

[ksnf3000]

Thanks for your reply Hassan2.

The negative sign indicates the loss the imaginary part suffers, right??

 

[Hassan2]

Thanks for your reply Hassan2.

The negative sign indicates the loss the imaginary part suffers, right??

that j is not supposed to be there. The parameters are real, so, the right hand side must be real too. When comparing their magnitudes, j and also -1 becomes 1.

 

[pmacias]

Hello ksnf3000,

Thank you for your question. The permittivity (ε) and conductivity (σ) values in conductors are related to the flow of electric current. When the electric current density becomes higher than the displacement current, it means that there is a large amount of charge moving through the conductor. This charge movement creates an electric field, which in turn induces a magnetic field. The displacement current, which is the rate of change of the electric field, becomes negligible compared to the actual electric current.

In this scenario, the value of ε is approximately equal to -jσ/ω, where j is the imaginary unit, σ is the conductivity, and ω is the angular frequency of the current. This relationship is known as the complex permittivity, which takes into account the effects of both the electric and magnetic fields in conductors. This value helps us to better understand and model the behavior of electric currents in conductors.

I hope this helps to answer your question. Best of luck with your studies in electronics engineering!

Best regards,