Magnitude of Wavevector Solution

STEP 0: Pre-Calculation Summary
Formula Used
Wave Vector = Angular Frequency*sqrt(Magnetic Permeability*Dielectric Permitivitty)
k = ω*sqrt(μ*∈')
This formula uses 1 Functions, 4 Variables
Functions Used
sqrt - Square root function, sqrt(Number)
Variables Used
Wave Vector - Wave Vector is a measure of the spatial frequency of a wave, representing the number of wavelengths per unit distance.
Angular Frequency - (Measured in Radian per Second) - Angular frequency is the rate of change of the phase of a sinusoidal waveform, measured in radians per unit time.
Magnetic Permeability - (Measured in Henry per Meter) - Magnetic Permeability is a property of a material's ability to respond to a magnetic field.It quantifies how easily a substance can be magnetized in the presence of a magnetic field.
Dielectric Permitivitty - (Measured in Farad per Meter) - Dielectric Permitivitty is a measure of a material's ability to permit the electric field lines to pass through it.
STEP 1: Convert Input(s) to Base Unit
Angular Frequency: 2.38 Radian per Second --> 2.38 Radian per Second No Conversion Required
Magnetic Permeability: 29.31 Henry per Centimeter --> 2931 Henry per Meter (Check conversion here)
Dielectric Permitivitty: 1.4 Microfarad per Millimeter --> 0.0014 Farad per Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
k = ω*sqrt(μ*∈') --> 2.38*sqrt(2931*0.0014)
Evaluating ... ...
k = 4.82113046494284
STEP 3: Convert Result to Output's Unit
4.82113046494284 --> No Conversion Required
FINAL ANSWER
4.82113046494284 4.82113 <-- Wave Vector
(Calculation completed in 00.004 seconds)

Credits

Created by Gowthaman N
Vellore Institute of Technology (VIT University), Chennai
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Vellore Institute of Technology (VIT Vellore), Vellore
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12 Guided Waves in Field Theory Calculators

Characteristic Impedance of Line
Go Characteristic Impedance = sqrt(Magnetic Permeability*pi*10^-7/Dielectric Permitivitty)*(Plate Distance/Plate Width)
Total Resistance of Coaxial Cable
Go Total Resistance of Coaxial Cable = 1/(2*pi*Skin Depth*Electrical Conductivity)*(1/Inner Radius of Coaxial Cable+1/Outer Radius of Coaxial Cable)
Inductance per unit Length of Coaxial Cable
Go Inductance per unit length of Coaxial Cable = Magnetic Permeability/2*pi*ln(Outer Radius of Coaxial Cable/Inner Radius of Coaxial Cable)
Conductance of Coaxial Cable
Go Conductance of Coaxial Cable = (2*pi*Electrical Conductivity)/ln(Outer Radius of Coaxial Cable/Inner Radius of Coaxial Cable)
Radian Cutoff Angular Frequency
Go Cutoff Angular Frequency = (Mode Number*pi*[c])/(Refractive Index*Plate Distance)
Inner Resistance of Coaxial Cable
Go Inner Resistance of Coaxial Cable = 1/(2*pi*Inner Radius of Coaxial Cable*Skin Depth*Electrical Conductivity)
Outer Resistance of Coaxial Cable
Go Outer Resistance of Coaxial Cable = 1/(2*pi*Skin Depth*Outer Radius of Coaxial Cable*Electrical Conductivity)
Inductance between Conductors
Go Conductor Inductance = Magnetic Permeability*pi*10^-7*Plate Distance/(Plate Width)
Magnitude of Wavevector
Go Wave Vector = Angular Frequency*sqrt(Magnetic Permeability*Dielectric Permitivitty)
Skin Effect Resistivity
Go Skin Effect Resistivity = 2/(Electrical Conductivity*Skin Depth*Plate Width)
Cutoff Wavelength
Go Cutoff Wavelength = (2*Refractive Index*Plate Distance)/Mode Number
Phase Velocity in Microstrip Line
Go Phase Velocity = [c]/sqrt(Dielectric Permitivitty)

Magnitude of Wavevector Formula

Wave Vector = Angular Frequency*sqrt(Magnetic Permeability*Dielectric Permitivitty)
k = ω*sqrt(μ*∈')

How does wavevector change with higher dielectric permittivity?

As the dielectric permittivity increases, the wavevector magnitude decreases due to the square root relationship in the dispersion relation. This signifies a reduction in the spatial frequency of the wave in the medium, influenced by the electromagnetic properties of the material.

How to Calculate Magnitude of Wavevector?

Magnitude of Wavevector calculator uses Wave Vector = Angular Frequency*sqrt(Magnetic Permeability*Dielectric Permitivitty) to calculate the Wave Vector, The Magnitude of Wavevector formula it relates the wavevector, which characterizes the spatial frequency and direction of the wave, to the angular frequency, magnetic permeability, and dielectric permittivity of the medium through which the wave is propagating. Wave Vector is denoted by k symbol.

How to calculate Magnitude of Wavevector using this online calculator? To use this online calculator for Magnitude of Wavevector, enter Angular Frequency (ω), Magnetic Permeability (μ) & Dielectric Permitivitty (∈') and hit the calculate button. Here is how the Magnitude of Wavevector calculation can be explained with given input values -> 4.82113 = 2.38*sqrt(2931*0.0014).

FAQ

What is Magnitude of Wavevector?
The Magnitude of Wavevector formula it relates the wavevector, which characterizes the spatial frequency and direction of the wave, to the angular frequency, magnetic permeability, and dielectric permittivity of the medium through which the wave is propagating and is represented as k = ω*sqrt(μ*∈') or Wave Vector = Angular Frequency*sqrt(Magnetic Permeability*Dielectric Permitivitty). Angular frequency is the rate of change of the phase of a sinusoidal waveform, measured in radians per unit time, Magnetic Permeability is a property of a material's ability to respond to a magnetic field.It quantifies how easily a substance can be magnetized in the presence of a magnetic field & Dielectric Permitivitty is a measure of a material's ability to permit the electric field lines to pass through it.
How to calculate Magnitude of Wavevector?
The Magnitude of Wavevector formula it relates the wavevector, which characterizes the spatial frequency and direction of the wave, to the angular frequency, magnetic permeability, and dielectric permittivity of the medium through which the wave is propagating is calculated using Wave Vector = Angular Frequency*sqrt(Magnetic Permeability*Dielectric Permitivitty). To calculate Magnitude of Wavevector, you need Angular Frequency (ω), Magnetic Permeability (μ) & Dielectric Permitivitty (∈'). With our tool, you need to enter the respective value for Angular Frequency, Magnetic Permeability & Dielectric Permitivitty 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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