How Is Electrical Permittivity Defined Mathematically Without Using Curls?

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    Explain Permittivity
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Discussion Overview

The discussion revolves around the mathematical definition of electrical permittivity, specifically seeking a derivation that does not involve the concept of curls. Participants explore the properties and implications of permittivity in various contexts, including its role in capacitance and its relationship with electric fields.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants describe permittivity as a constant related to the electrical properties of a medium, appearing in Coulomb's law and the formula for the speed of light.
  • One participant provides the formula for the capacitance of a rectangular capacitor, indicating how permittivity is involved in calculating capacitance.
  • Another participant expresses confusion between permittivity and permeability, suggesting a mix-up in terminology.
  • A participant questions the existence of a derivation for permittivity from first principles, stating that permittivity and permeability are constants rather than derived quantities.
  • One viewpoint suggests that permittivity can be understood as the ability of a medium to allow conductors at an electric potential to accumulate charges on their surface.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the derivation of permittivity, with some asserting it is a constant while others seek a theoretical foundation for its definition. The discussion remains unresolved regarding the derivation and conceptual understanding of permittivity.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the nature of permittivity and its derivation, as well as the potential confusion between related concepts such as permittivity and permeability.

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Electrical permittivity...in mathematical terms, i.e I need the derivation...WITHOUT using 'curls'.



Didn't find it online.
 
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The permittivity of a medium is a constant that is connected to the electrical properties of that medium.Amongst other places it appears in Coulombs law and along with permittivity( a magnetic constant ) the formula for the speed of light.
 
Dadface said:
The permittivity of a medium is a constant that is connected to the electrical properties of that medium.Amongst other places it appears in Coulombs law and along with permittivity**( a magnetic constant ) the formula for the speed of light.

In mks units, the capacitance of a rectangular capacitor of relative permittivity e, separation d, and area A is

C = e e0 A/d Farads

where e is relative permittivity (unitless)
e0 is the permittivity of free space, 8.85 x 10-12 Farads per meter.

**The magnetic constant is permeability.
 
Bob S said:
In mks units, the capacitance of a rectangular capacitor of relative permittivity e, separation d, and area A is

C = e e0 A/d Farads

where e is relative permittivity (unitless)
e0 is the permittivity of free space, 8.85 x 10-12 Farads per meter.

**The magnetic constant is permeability.

Thank you Bob I got my mittivity mixed up with eability.I would blame it on the beer but I haven't had one yet.
 
I'm asking the derivation of permittivity, not relative.And pls explain a bit of theory also.
 
What do you mean derivation? I'm not aware of any derivation of permittivity or permeability from first principles, at least not classically. The two are constants. Permittivity can be thought of as describing the capacitance of the medium. Even vacuum can be thought of as having a capacitance. In a material, the permittivity describes the ability to store extra energy. This is done by polarizing the molecules in the material. The induced dipoles allow you to store more energy in the material.
 
In my opinion, permittivity can be defined as the ability of a medium to allow conductors at an electric potential to accumulate electrical charges on it's surface.
 

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