Local field using Incident Field and Polarization Calculator

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Size Effects on Structure and Morphology of Free or Supported Nanoparticles

✖The Incident Field is the subtraction of the polarization factor from the local field in the Lorentz–Lorenz expression.ⓘ Incident Field [E]			+10% -10%
✖The Polarization due to Sphere is the the action or process of affecting radiation and especially light so that the vibrations of the wave assume a definite form.ⓘ Polarization due to Sphere [P_sph]			+10% -10%
✖The Real Dielectric Constant is the ratio of the electric permeability of a material to the electric permeability of a vacuum.ⓘ Real Dielectric Constant [ε_m]			+10% -10%
✖The Vacuum Dielectric Constant is the ratio of the permittivity of a substance to the permittivity of space or vacuum.ⓘ Vacuum Dielectric Constant [ε₀]			+10% -10%

✖The Local Field is related to the incident field due in the Lorentz–Lorenz expression and also related to the polarization.ⓘ Local field using Incident Field and Polarization [E₁]

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Formula

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Local field using Incident Field and Polarization

Formula

`"E"_{"1"} = "E"+("P"_{"sph"}/(3*"ε"_{"m"}*"ε"_{"0"}))`

Example

`"40.00926J"="40J"+("50C/m²"/(3*"60"*"30"))`

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Local field using Incident Field and Polarization Solution

STEP 0: Pre-Calculation Summary

Formula Used

Local Field = Incident Field+(Polarization due to Sphere/(3*Real Dielectric Constant*Vacuum Dielectric Constant))
E₁ = E+(P_sph/(3*ε_m*ε₀))
This formula uses 5 Variables

Variables Used

Local Field - (Measured in Joule) - The Local Field is related to the incident field due in the Lorentz–Lorenz expression and also related to the polarization.
Incident Field - (Measured in Joule) - The Incident Field is the subtraction of the polarization factor from the local field in the Lorentz–Lorenz expression.
Polarization due to Sphere - (Measured in Coulomb per Square Meter) - The Polarization due to Sphere is the the action or process of affecting radiation and especially light so that the vibrations of the wave assume a definite form.
Real Dielectric Constant - The Real Dielectric Constant is the ratio of the electric permeability of a material to the electric permeability of a vacuum.
Vacuum Dielectric Constant - The Vacuum Dielectric Constant is the ratio of the permittivity of a substance to the permittivity of space or vacuum.

STEP 1: Convert Input(s) to Base Unit

Incident Field: 40 Joule --> 40 Joule No Conversion Required
Polarization due to Sphere: 50 Coulomb per Square Meter --> 50 Coulomb per Square Meter No Conversion Required
Real Dielectric Constant: 60 --> No Conversion Required
Vacuum Dielectric Constant: 30 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E₁ = E+(P_sph/(3*ε_m*ε₀)) --> 40+(50/(3*60*30))

Evaluating ... ...

E₁ = 40.0092592592593

STEP 3: Convert Result to Output's Unit

40.0092592592593 Joule --> No Conversion Required

FINAL ANSWER

40.0092592592593 ≈ 40.00926 Joule <-- Local Field

(Calculation completed in 00.004 seconds)

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< 23 Optical Properties of Metallic Nanoparticles Calculators

Total Polarization of Composite Material using Dielectric Constants and Incident Field

Go Total polarization of Composite Material = Vacuum Dielectric Constant*(Real Dielectric Constant-1)*Incident Field+((Volume Fraction*Dipole Moment of Sphere)/Volume of Nanoparticle)

Total Collision Rate using Intrinsic Electron Collision Frequency

Go Total Collision Rate = Intrinsic Electron Collision Rate+(Proportionality Factor*Fermi Speed of Electron)/Diameter of Spheres

Intrinsic Electron Collision Frequency using Total Collision Rate

Go Intrinsic Electron Collision Rate = Total Collision Rate-(Proportionality Factor*Fermi Speed of Electron)/Diameter of Spheres

Local field using Incident Field and Polarization

Go Local Field = Incident Field+(Polarization due to Sphere/(3*Real Dielectric Constant*Vacuum Dielectric Constant))

Incident Field using Local Field and Polarization

Go Incident Field = Local Field-(Polarization due to Sphere/(3*Real Dielectric Constant*Vacuum Dielectric Constant))

Polarization due to Sphere using Local field and Incident Field

Go Polarization due to Sphere = (Local Field-Incident Field)*3*Real Dielectric Constant*Vacuum Dielectric Constant

Polarization Due to Metallic Particle using Dielectric Constants and Incident Field

Go Polarization due to Metallic Particle = Vacuum Dielectric Constant*(Real Dielectric Constant-1)*Incident Field

Average Electron Density using Nanoparticle Density and Spill-out Amplitude

Go Average Electron Density = Electron Density*(1-(3*Spill Out Amplitude/Nanoparticle Diameter))

Electron Density using Average Electron Density and Spill-out Amplitude

Go Electron Density = Average Electron Density/(1-(3*Spill Out Amplitude/Nanoparticle Diameter))

Volume Fraction using Polarization and Dipole Moment of Sphere

Go Volume Fraction = Polarization due to Sphere*Volume of Nanoparticle/Dipole Moment of Sphere

Polarization due to Sphere using Dipole moment of Sphere

Go Polarization due to Sphere = Volume Fraction*Dipole Moment of Sphere/Volume of Nanoparticle

Dipole moment of Sphere using Polarization due to Sphere

Go Dipole Moment of Sphere = Polarization due to Sphere*Volume of Nanoparticle/Volume Fraction

Average Electron Density using Electron Density and Electron diameter

Go Average Electron Density = (Electron Density*Nanoparticle Diameter^3)/Electron Diameter^3

Electron Density using Average Electron Density and Electron diameter

Go Electron Density = Average Electron Density*Electron Diameter^3/Nanoparticle Diameter^3

Number of Nanoparticles using Volume Fraction and Volume of Nanoparticle

Go Number of Nanoparticles = (Volume Fraction*Volume of Material)/Volume of Nanoparticle

Volume Fraction using Volume of Nanoparticles

Go Volume Fraction = (Number of Nanoparticles*Volume of Nanoparticle)/Volume of Material

Volume of Nanoparticles using Volume Fraction

Go Volume of Nanoparticle = (Volume Fraction*Volume of Material)/Number of Nanoparticles

Total Polarization of Composite Material using Polarization due to Metallic Particle and Sphere

Go Total polarization of Composite Material = Polarization due to Metallic Particle+Polarization due to Sphere

Polarization Due to Metallic Particle using Total Polarization and Polarization Due to Sphere

Go Polarization due to Metallic Particle = Total polarization of Composite Material-Polarization due to Sphere

Polarization Due to Sphere using Polarization Due to Metallic Particle and Total Polarization

Go Polarization due to Sphere = Total polarization of Composite Material-Polarization due to Metallic Particle

Nanoparticle Diameter using Electron Diameter and Spill-out Amplitude

Go Nanoparticle Diameter = Electron Diameter-Spill Out Amplitude

Electron Diameter using Nanoparticle Diameter and Spill-out Amplitude

Go Electron Diameter = Nanoparticle Diameter+Spill Out Amplitude

Spill-out Amplitude using Nanoparticle Diameter and Electron Diameter

Go Spill Out Amplitude = Electron Diameter-Nanoparticle Diameter

Local field using Incident Field and Polarization Formula

Local Field = Incident Field+(Polarization due to Sphere/(3*Real Dielectric Constant*Vacuum Dielectric Constant))
E₁ = E+(P_sph/(3*ε_m*ε₀))

What is Transmission?

A transmission, also known as a gearbox, is a mechanical device that uses gears to change the speed or direction of rotation in a machine.

How to Calculate Local field using Incident Field and Polarization?

Local field using Incident Field and Polarization calculator uses Local Field = Incident Field+(Polarization due to Sphere/(3*Real Dielectric Constant*Vacuum Dielectric Constant)) to calculate the Local Field, The Local field using Incident Field and Polarization formula is defined as the sum of the incident field by the Lorentz–Lorenz expression and the polarization factor. Local Field is denoted by E₁ symbol.

How to calculate Local field using Incident Field and Polarization using this online calculator? To use this online calculator for Local field using Incident Field and Polarization, enter Incident Field (E), Polarization due to Sphere (P_sph), Real Dielectric Constant (ε_m) & Vacuum Dielectric Constant (ε₀) and hit the calculate button. Here is how the Local field using Incident Field and Polarization calculation can be explained with given input values -> 40.00926 = 40+(50/(3*60*30)).

FAQ

What is Local field using Incident Field and Polarization?

The Local field using Incident Field and Polarization formula is defined as the sum of the incident field by the Lorentz–Lorenz expression and the polarization factor and is represented as E₁ = E+(P_sph/(3*ε_m*ε₀)) or Local Field = Incident Field+(Polarization due to Sphere/(3*Real Dielectric Constant*Vacuum Dielectric Constant)). The Incident Field is the subtraction of the polarization factor from the local field in the Lorentz–Lorenz expression, The Polarization due to Sphere is the the action or process of affecting radiation and especially light so that the vibrations of the wave assume a definite form, The Real Dielectric Constant is the ratio of the electric permeability of a material to the electric permeability of a vacuum & The Vacuum Dielectric Constant is the ratio of the permittivity of a substance to the permittivity of space or vacuum.

How to calculate Local field using Incident Field and Polarization?

The Local field using Incident Field and Polarization formula is defined as the sum of the incident field by the Lorentz–Lorenz expression and the polarization factor is calculated using Local Field = Incident Field+(Polarization due to Sphere/(3*Real Dielectric Constant*Vacuum Dielectric Constant)). To calculate Local field using Incident Field and Polarization, you need Incident Field (E), Polarization due to Sphere (P_sph), Real Dielectric Constant (ε_m) & Vacuum Dielectric Constant (ε₀). With our tool, you need to enter the respective value for Incident Field, Polarization due to Sphere, Real Dielectric Constant & Vacuum Dielectric Constant and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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