Polarization Due to Metallic Particle using Dielectric Constants and Incident Field Calculator

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Optical Properties of Metallic Nanoparticles

Electronic Structure in Clusters and Nanoparticles

Mechanical and Nanomechanical Properties

Size Effects on Structure and Morphology of Free or Supported Nanoparticles

✖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 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 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 Metallic Particle is the action or process of affecting radiation and especially light in a metallic particle so that the vibrations of the wave assume a definite form.ⓘ Polarization Due to Metallic Particle using Dielectric Constants and Incident Field [P_m]

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Formula

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Polarization Due to Metallic Particle using Dielectric Constants and Incident Field

Formula

`"P"_{"m"} = "ε"_{"0"}*("ε"_{"m"}-1)*"E"`

Example

`"70800C/m²"="30"*("60"-1)*"40J"`

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Polarization Due to Metallic Particle using Dielectric Constants and Incident Field Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polarization due to Metallic Particle = Vacuum Dielectric Constant*(Real Dielectric Constant-1)*Incident Field
P_m = ε₀*(ε_m-1)*E
This formula uses 4 Variables

Variables Used

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

STEP 1: Convert Input(s) to Base Unit

Vacuum Dielectric Constant: 30 --> No Conversion Required
Real Dielectric Constant: 60 --> No Conversion Required
Incident Field: 40 Joule --> 40 Joule No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_m = ε₀*(ε_m-1)*E --> 30*(60-1)*40

Evaluating ... ...

P_m = 70800

STEP 3: Convert Result to Output's Unit

70800 Coulomb per Square Meter --> No Conversion Required

FINAL ANSWER

70800 Coulomb per Square Meter <-- Polarization due to Metallic Particle

(Calculation completed in 00.020 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

Polarization Due to Metallic Particle using Dielectric Constants and Incident Field Formula

Polarization due to Metallic Particle = Vacuum Dielectric Constant*(Real Dielectric Constant-1)*Incident Field
P_m = ε₀*(ε_m-1)*E

What is oscillation?

Oscillation refers to the repetitive or periodic variation, typically in time, of some measure about a central value or between two or more different states.

How to Calculate Polarization Due to Metallic Particle using Dielectric Constants and Incident Field?

Polarization Due to Metallic Particle using Dielectric Constants and Incident Field calculator uses Polarization due to Metallic Particle = Vacuum Dielectric Constant*(Real Dielectric Constant-1)*Incident Field to calculate the Polarization due to Metallic Particle, The Polarization Due to Metallic Particle using Dielectric Constants and Incident Field formula is defined as the distortion, deformation or polarization of an anion when two oppositely charged ions approach each other in the presence of metallic particle; which can be calculated as the product of vacuum dielectric constant, incident field and subtraction of 1 from real dielectric constant. Polarization due to Metallic Particle is denoted by P_m symbol.

How to calculate Polarization Due to Metallic Particle using Dielectric Constants and Incident Field using this online calculator? To use this online calculator for Polarization Due to Metallic Particle using Dielectric Constants and Incident Field, enter Vacuum Dielectric Constant (ε₀), Real Dielectric Constant (ε_m) & Incident Field (E) and hit the calculate button. Here is how the Polarization Due to Metallic Particle using Dielectric Constants and Incident Field calculation can be explained with given input values -> 70800 = 30*(60-1)*40.

FAQ

What is Polarization Due to Metallic Particle using Dielectric Constants and Incident Field?

The Polarization Due to Metallic Particle using Dielectric Constants and Incident Field formula is defined as the distortion, deformation or polarization of an anion when two oppositely charged ions approach each other in the presence of metallic particle; which can be calculated as the product of vacuum dielectric constant, incident field and subtraction of 1 from real dielectric constant and is represented as P_m = ε₀*(ε_m-1)*E or Polarization due to Metallic Particle = Vacuum Dielectric Constant*(Real Dielectric Constant-1)*Incident Field. The Vacuum Dielectric Constant is the ratio of the permittivity of a substance to the permittivity of space or vacuum, The Real Dielectric Constant is the ratio of the electric permeability of a material to the electric permeability of a vacuum & The Incident Field is the subtraction of the polarization factor from the local field in the Lorentz–Lorenz expression.

How to calculate Polarization Due to Metallic Particle using Dielectric Constants and Incident Field?

The Polarization Due to Metallic Particle using Dielectric Constants and Incident Field formula is defined as the distortion, deformation or polarization of an anion when two oppositely charged ions approach each other in the presence of metallic particle; which can be calculated as the product of vacuum dielectric constant, incident field and subtraction of 1 from real dielectric constant is calculated using Polarization due to Metallic Particle = Vacuum Dielectric Constant*(Real Dielectric Constant-1)*Incident Field. To calculate Polarization Due to Metallic Particle using Dielectric Constants and Incident Field, you need Vacuum Dielectric Constant (ε₀), Real Dielectric Constant (ε_m) & Incident Field (E). With our tool, you need to enter the respective value for Vacuum Dielectric Constant, Real Dielectric Constant & Incident Field and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Polarization due to Metallic Particle?

In this formula, Polarization due to Metallic Particle uses Vacuum Dielectric Constant, Real Dielectric Constant & Incident Field. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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