Poynting Vector Magnitude Calculator

↳

Electronics

Chemical Engineering

Civil

Electrical

Electronics and Instrumentation

Materials Science

Mechanical

Production Engineering

⤿

Electromagnetic Radiation and Antennas

Guided Waves in Field Theory

Magnetic Forces and Materials

✖Dipole Current is the current flowing through a hertzian dipole antenna.ⓘ Dipole Current [I_d]			+10% -10%
✖Wavenumber represents the spatial frequency of a wave, signifying how many times the wave pattern repeats within a specific unit distance.ⓘ Wavenumber [k]			+10% -10%
✖Source Distance represents the distance from the point of observation to the source of the wave.ⓘ Source Distance [d]			+10% -10%
✖Intrinsic Impedance is a property of a medium that represents the resistance it offers to the propagation of electromagnetic waves.ⓘ Intrinsic Impedance [η]			+10% -10%
✖Polar Angle is a coordinate in a polar coordinate system that measures the angle between a point and a fixed reference direction, typically the positive x-axis.ⓘ Polar Angle [θ]			+10% -10%

✖Poynting Vector is a vector quantity that describes the directional energy flux density of an electromagnetic field.ⓘ Poynting Vector Magnitude [S_r]

⎘ Copy

👎

Formula

✖

Poynting Vector Magnitude

Formula

`"S"_{"r"} = 1/2*(("I"_{"d"}*"k"*"d")/(4*pi))^2*"η"*(sin("θ"))^2`

Example

`"11954.34W/m²"=1/2*(("23.4A"*"5"*"6.4m")/(4*pi))^2*"9.3Ω"*(sin("45rad"))^2`

Calculator

LaTeX

Reset

👍

Download Electronics Formula PDF PDF Image

Poynting Vector Magnitude Solution

STEP 0: Pre-Calculation Summary

Formula Used

Poynting Vector = 1/2*((Dipole Current*Wavenumber*Source Distance)/(4*pi))^2*Intrinsic Impedance*(sin(Polar Angle))^2
S_r = 1/2*((I_d*k*d)/(4*pi))^2*η*(sin(θ))^2
This formula uses 1 Constants, 1 Functions, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Poynting Vector - (Measured in Watt per Square Meter) - Poynting Vector is a vector quantity that describes the directional energy flux density of an electromagnetic field.
Dipole Current - (Measured in Ampere) - Dipole Current is the current flowing through a hertzian dipole antenna.
Wavenumber - Wavenumber represents the spatial frequency of a wave, signifying how many times the wave pattern repeats within a specific unit distance.
Source Distance - (Measured in Meter) - Source Distance represents the distance from the point of observation to the source of the wave.
Intrinsic Impedance - (Measured in Ohm) - Intrinsic Impedance is a property of a medium that represents the resistance it offers to the propagation of electromagnetic waves.
Polar Angle - (Measured in Radian) - Polar Angle is a coordinate in a polar coordinate system that measures the angle between a point and a fixed reference direction, typically the positive x-axis.

STEP 1: Convert Input(s) to Base Unit

Dipole Current: 23.4 Ampere --> 23.4 Ampere No Conversion Required
Wavenumber: 5 --> No Conversion Required
Source Distance: 6.4 Meter --> 6.4 Meter No Conversion Required
Intrinsic Impedance: 9.3 Ohm --> 9.3 Ohm No Conversion Required
Polar Angle: 45 Radian --> 45 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_r = 1/2*((I_d*k*d)/(4*pi))^2*η*(sin(θ))^2 --> 1/2*((23.4*5*6.4)/(4*pi))^2*9.3*(sin(45))^2

Evaluating ... ...

S_r = 11954.3382860445

STEP 3: Convert Result to Output's Unit

11954.3382860445 Watt per Square Meter --> No Conversion Required

FINAL ANSWER

11954.3382860445 ≈ 11954.34 Watt per Square Meter <-- Poynting Vector

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Electronics » Electromagnetic Field Theory » Electromagnetic Radiation and Antennas » Poynting Vector Magnitude

Credits

Created by Santhosh Yadav

Dayananda Sagar College Of Engineering (DSCE), Banglore

Santhosh Yadav has created this Calculator and 50+ more calculators!

Verified by Ritwik Tripathi

Vellore Institute of Technology (VIT Vellore), Vellore

Ritwik Tripathi has verified this Calculator and 100+ more calculators!

< 17 Electromagnetic Radiation and Antennas Calculators

Average Power Density of Half-Wave Dipole

Go Average Power Density = (0.609*Intrinsic Impedance of Medium*Amplitude of Oscillating Current^2)/(4*pi^2*Radial Distance From Antenna^2)*sin((((Angular Frequency of Half Wave Dipole*Time)-(pi/Length of Antenna)*Radial Distance From Antenna))*pi/180)^2

Magnetic Field for Hertzian Dipole

Go Magnetic Field Component = (1/Dipole Distance)^2*(cos(2*pi*Dipole Distance/Wavelength of Dipole)+2*pi*Dipole Distance/Wavelength of Dipole*sin(2*pi*Dipole Distance/Wavelength of Dipole))

Maximum Power Density of Half-Wave Dipole

Go Maximum Power Density = (Intrinsic Impedance of Medium*Amplitude of Oscillating Current^2)/(4*pi^2*Radial Distance From Antenna^2)*sin((((Angular Frequency of Half Wave Dipole*Time)-(pi/Length of Antenna)*Radial Distance From Antenna))*pi/180)^2

Power Radiated by Half-Wave Dipole

Go Power Radiated by Half-wave Dipole = ((0.609*Intrinsic Impedance of Medium*(Amplitude of Oscillating Current)^2)/pi)*sin(((Angular Frequency of Half Wave Dipole*Time)-((pi/Length of Antenna)*Radial Distance From Antenna))*pi/180)^2

Power that Crosses Surface of Sphere

Go Power Crossed at Sphere Surface = pi*((Amplitude of Oscillating Current*Wavenumber*Short Antenna Length)/(4*pi))^2*Intrinsic Impedance of Medium*(int(sin(Theta)^3*x,x,0,pi))

Electric Field due to N Point Charges

Go Electric Field due to N Point Charges = sum(x,1,Number of Point Charges,(Charge)/(4*pi*[Permitivity-vacuum]*(Distance from Electric Field-Charge Distance)^2))

Poynting Vector Magnitude

Go Poynting Vector = 1/2*((Dipole Current*Wavenumber*Source Distance)/(4*pi))^2*Intrinsic Impedance*(sin(Polar Angle))^2

Total Radiated Power in Free Space

Go Total Radiated Power in Free Space = 30*Amplitude of Oscillating Current^2*int((Dipole Antenna Pattern Function)^2*sin(Theta)*x,x,0,pi)

Radiated Resistance

Go Radiation Resistance = 60*(int((Dipole Antenna Pattern Function)^2*sin(Theta)*x,x,0,pi))

Time Average Radiated Power of Half-Wave Dipole

Go Time Average Radiated Power = (((Amplitude of Oscillating Current)^2)/2)*((0.609*Intrinsic Impedance of Medium)/pi)

Polarization

Go Polarization = Electric Susceptibility*[Permitivity-vacuum]*Electric Field Strength

Radiation Resistance of Half-Wave Dipole

Go Radiation Resistance of Half-wave Dipole = (0.609*Intrinsic Impedance of Medium)/pi

Directivity of Half-Wave Dipole

Go Directivity of Half Wave Dipole = Maximum Power Density/Average Power Density

Electric Field for Hertzian Dipole

Go Electric Field Component = Intrinsic Impedance*Magnetic Field Component

Radiation Efficiency of Antenna

Go Radiation Efficiency of Antenna = Maximum Gain/Maximum Directivity

Average Power

Go Average Power = 1/2*Sinusoidal Current^2*Radiation Resistance

Radiation Resistance of Antenna

Go Radiation Resistance = 2*Average Power/Sinusoidal Current^2

Poynting Vector Magnitude Formula

Poynting Vector = 1/2*((Dipole Current*Wavenumber*Source Distance)/(4*pi))^2*Intrinsic Impedance*(sin(Polar Angle))^2
S_r = 1/2*((I_d*k*d)/(4*pi))^2*η*(sin(θ))^2

How does intrinsic impedance affect Poynting vector magnitude in a solar cell array?

A higher intrinsic impedance of the solar cell material signifies greater resistance to the incoming electromagnetic wave. This leads to a decrease in the Poynting vector magnitude, indicating less energy flow per unit area through the material.

How to Calculate Poynting Vector Magnitude?

Poynting Vector Magnitude calculator uses Poynting Vector = 1/2*((Dipole Current*Wavenumber*Source Distance)/(4*pi))^2*Intrinsic Impedance*(sin(Polar Angle))^2 to calculate the Poynting Vector, The Poynting Vector Magnitude defines the magnitude of the Poynting vector for a spherical electromagnetic wave emanating from a dipole antenna. Poynting Vector is denoted by S_r symbol.

How to calculate Poynting Vector Magnitude using this online calculator? To use this online calculator for Poynting Vector Magnitude, enter Dipole Current (I_d), Wavenumber (k), Source Distance (d), Intrinsic Impedance (η) & Polar Angle (θ) and hit the calculate button. Here is how the Poynting Vector Magnitude calculation can be explained with given input values -> 11954.34 = 1/2*((23.4*5*6.4)/(4*pi))^2*9.3*(sin(45))^2.

FAQ

What is Poynting Vector Magnitude?

The Poynting Vector Magnitude defines the magnitude of the Poynting vector for a spherical electromagnetic wave emanating from a dipole antenna and is represented as S_r = 1/2*((I_d*k*d)/(4*pi))^2*η*(sin(θ))^2 or Poynting Vector = 1/2*((Dipole Current*Wavenumber*Source Distance)/(4*pi))^2*Intrinsic Impedance*(sin(Polar Angle))^2. Dipole Current is the current flowing through a hertzian dipole antenna, Wavenumber represents the spatial frequency of a wave, signifying how many times the wave pattern repeats within a specific unit distance, Source Distance represents the distance from the point of observation to the source of the wave, Intrinsic Impedance is a property of a medium that represents the resistance it offers to the propagation of electromagnetic waves & Polar Angle is a coordinate in a polar coordinate system that measures the angle between a point and a fixed reference direction, typically the positive x-axis.

How to calculate Poynting Vector Magnitude?

The Poynting Vector Magnitude defines the magnitude of the Poynting vector for a spherical electromagnetic wave emanating from a dipole antenna is calculated using Poynting Vector = 1/2*((Dipole Current*Wavenumber*Source Distance)/(4*pi))^2*Intrinsic Impedance*(sin(Polar Angle))^2. To calculate Poynting Vector Magnitude, you need Dipole Current (I_d), Wavenumber (k), Source Distance (d), Intrinsic Impedance (η) & Polar Angle (θ). With our tool, you need to enter the respective value for Dipole Current, Wavenumber, Source Distance, Intrinsic Impedance & Polar Angle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search