Total Polarization of Composite Material 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 Volume Fraction is the total volume of all the nanoparticles divided by the volume of the material here.ⓘ Volume Fraction [p]			+10% -10%
✖The Dipole Moment of Sphere is a measure of the separation of positive and negative electrical charges within a system.ⓘ Dipole Moment of Sphere [p_s]			+10% -10%
✖The Volume of Nanoparticle is the particular volume of a single nanoparticle of interest.ⓘ Volume of Nanoparticle [V_np]			+10% -10%

✖The Total polarization of Composite Material is the action or process of affecting radiation and especially light so that the vibrations of the wave assume a definite form.ⓘ Total Polarization of Composite Material using Dielectric Constants and Incident Field [P]

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Formula

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Total Polarization of Composite Material using Dielectric Constants and Incident Field

Formula

`"P" = "ε"_{"0"}*("ε"_{"m"}-1)*"E"+(("p"*"p"_{"s"})/"V"_{"np"})`

Example

`"1.7E^29C/m²"="30"*("60"-1)*"40J"+(("50"*"100C*m")/"30nm³")`

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Total Polarization of Composite Material using Dielectric Constants and Incident Field Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total polarization of Composite Material = Vacuum Dielectric Constant*(Real Dielectric Constant-1)*Incident Field+((Volume Fraction*Dipole Moment of Sphere)/Volume of Nanoparticle)
P = ε₀*(ε_m-1)*E+((p*p_s)/V_np)
This formula uses 7 Variables

Variables Used

Total polarization of Composite Material - (Measured in Coulomb per Square Meter) - The Total polarization of Composite Material is the action or process of affecting radiation and especially light 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.
Volume Fraction - The Volume Fraction is the total volume of all the nanoparticles divided by the volume of the material here.
Dipole Moment of Sphere - (Measured in Coulomb Meter) - The Dipole Moment of Sphere is a measure of the separation of positive and negative electrical charges within a system.
Volume of Nanoparticle - (Measured in Cubic Meter) - The Volume of Nanoparticle is the particular volume of a single nanoparticle of interest.

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
Volume Fraction: 50 --> No Conversion Required
Dipole Moment of Sphere: 100 Coulomb Meter --> 100 Coulomb Meter No Conversion Required
Volume of Nanoparticle: 30 Cubic Nanometer --> 3E-26 Cubic Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P = ε₀*(ε_m-1)*E+((p*p_s)/V_np) --> 30*(60-1)*40+((50*100)/3E-26)

Evaluating ... ...

P = 1.66666666666667E+29

STEP 3: Convert Result to Output's Unit

1.66666666666667E+29 Coulomb per Square Meter --> No Conversion Required

FINAL ANSWER

1.66666666666667E+29 ≈ 1.7E+29 Coulomb per Square Meter <-- Total polarization of Composite Material

(Calculation completed in 00.004 seconds)

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national institute of technology meghalaya (NIT Meghalaya), Shillong

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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

Total Polarization of Composite Material using Dielectric Constants and Incident Field Formula

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 Total Polarization of Composite Material using Dielectric Constants and Incident Field?

Total Polarization of Composite Material using Dielectric Constants and Incident Field calculator uses Total polarization of Composite Material = Vacuum Dielectric Constant*(Real Dielectric Constant-1)*Incident Field+((Volume Fraction*Dipole Moment of Sphere)/Volume of Nanoparticle) to calculate the Total polarization of Composite Material, The Total Polarization of Composite Material using Dielectric Constants and Incident Field formula is defined as the sum of polarization due to metallic particle and polarization due to sphere, where we can use dielectric constants and incident field to calculate polarization due to metallic particle. Total polarization of Composite Material is denoted by P symbol.

How to calculate Total Polarization of Composite Material using Dielectric Constants and Incident Field using this online calculator? To use this online calculator for Total Polarization of Composite Material using Dielectric Constants and Incident Field, enter Vacuum Dielectric Constant (ε₀), Real Dielectric Constant (ε_m), Incident Field (E), Volume Fraction (p), Dipole Moment of Sphere (p_s) & Volume of Nanoparticle (V_np) and hit the calculate button. Here is how the Total Polarization of Composite Material using Dielectric Constants and Incident Field calculation can be explained with given input values -> 1.7E+29 = 30*(60-1)*40+((50*100)/3E-26).

FAQ

What is Total Polarization of Composite Material using Dielectric Constants and Incident Field?

The Total Polarization of Composite Material using Dielectric Constants and Incident Field formula is defined as the sum of polarization due to metallic particle and polarization due to sphere, where we can use dielectric constants and incident field to calculate polarization due to metallic particle and is represented as P = ε₀*(ε_m-1)*E+((p*p_s)/V_np) or Total polarization of Composite Material = Vacuum Dielectric Constant*(Real Dielectric Constant-1)*Incident Field+((Volume Fraction*Dipole Moment of Sphere)/Volume of Nanoparticle). 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, The Volume Fraction is the total volume of all the nanoparticles divided by the volume of the material here, The Dipole Moment of Sphere is a measure of the separation of positive and negative electrical charges within a system & The Volume of Nanoparticle is the particular volume of a single nanoparticle of interest.

How to calculate Total Polarization of Composite Material using Dielectric Constants and Incident Field?

The Total Polarization of Composite Material using Dielectric Constants and Incident Field formula is defined as the sum of polarization due to metallic particle and polarization due to sphere, where we can use dielectric constants and incident field to calculate polarization due to metallic particle is calculated using Total polarization of Composite Material = Vacuum Dielectric Constant*(Real Dielectric Constant-1)*Incident Field+((Volume Fraction*Dipole Moment of Sphere)/Volume of Nanoparticle). To calculate Total Polarization of Composite Material using Dielectric Constants and Incident Field, you need Vacuum Dielectric Constant (ε₀), Real Dielectric Constant (ε_m), Incident Field (E), Volume Fraction (p), Dipole Moment of Sphere (p_s) & Volume of Nanoparticle (V_np). With our tool, you need to enter the respective value for Vacuum Dielectric Constant, Real Dielectric Constant, Incident Field, Volume Fraction, Dipole Moment of Sphere & Volume of Nanoparticle 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 Total polarization of Composite Material?

In this formula, Total polarization of Composite Material uses Vacuum Dielectric Constant, Real Dielectric Constant, Incident Field, Volume Fraction, Dipole Moment of Sphere & Volume of Nanoparticle. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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