Permittivity values in conductors

In summary: So, the j has no physical meaning, it is just a mathematical artifact.In summary, the value of ε≈-jσ/ω when the electric current density becomes greater than the displacement current for a conductor. This is due to the imaginary part suffering a loss, which is represented by the negative sign. However, this j has no physical meaning and is simply a mathematical artifact.
  • #1
ksnf3000
5
0
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
 
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  • #2
ksnf3000 said:
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 :

[itex]J=σE[/itex]

displacement current density :

[itex]J_{d}=\frac{\partial D}{\partial t}[/itex]

for a steady stead sinusoidal field,

[itex]J_{d}=jωD=jωεE[/itex]

the ratio is [itex]\frac{ωε}{σ}[/itex]

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

I hope that helps.
 
  • #3
Thanks for your reply Hassan2.

The negative sign indicates the loss the imaginary part suffers, right??
 
  • #4
ksnf3000 said:
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.
 
  • #5


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,

 

Related to Permittivity values in conductors

1. What is permittivity?

Permittivity is a physical property of a material that describes how much it can be polarized in response to an applied electric field.

2. What is the difference between permittivity in conductors and insulators?

Permittivity in conductors is much higher than in insulators, meaning that conductors are easier to polarize and have higher capacitance. This is because conductors have more mobile charges that can respond to an electric field.

3. How is permittivity in conductors measured?

Permittivity in conductors is typically measured using a capacitance meter. The conductor is placed in a parallel plate capacitor and the capacitance is measured. The permittivity can then be calculated using the capacitance and the area and distance between the plates.

4. Can permittivity change in conductors?

Yes, permittivity in conductors can change with different factors such as temperature, frequency, and composition of the material. For example, as the temperature increases, the permittivity of a conductor typically decreases.

5. How does permittivity in conductors affect the performance of electronic devices?

Permittivity in conductors plays a crucial role in the design and performance of electronic devices. It affects the capacitance and impedance of circuits, which can impact the speed and efficiency of the device. High permittivity materials are often used in capacitors and other components to improve their performance.

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