## 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
Sr = 1/2*((Id*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: 5.1 --> 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
Sr = 1/2*((Id*k*d)/(4*pi))^2*η*(sin(θ))^2 --> 1/2*((23.4*5.1*6.4)/(4*pi))^2*9.3*(sin(45))^2
Evaluating ... ...
Sr = 12437.2935528007
STEP 3: Convert Result to Output's Unit
12437.2935528007 Watt per Square Meter -->12.4372935528007 Kilowatt per Square Meter (Check conversion ​here)
12.4372935528007 12.43729 Kilowatt per Square Meter <-- Poynting Vector
(Calculation completed in 00.004 seconds)
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## 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
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## <Electromagnetic Radiation and Antennas Calculators

Poynting Vector Magnitude
​ Go Poynting Vector = 1/2*((Dipole Current*Wavenumber*Source Distance)/(4*pi))^2*Intrinsic Impedance*(sin(Polar Angle))^2
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
Sr = 1/2*((Id*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, Poynting Vector Magnitude represents the rate of energy flow per unit area in an electromagnetic field, calculated as the cross product of the electric and magnetic fields, measured in watts per square meter. Poynting Vector is denoted by Sr symbol.

How to calculate Poynting Vector Magnitude using this online calculator? To use this online calculator for Poynting Vector Magnitude, enter Dipole Current (Id), 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 -> 12437.29 = 1/2*((23.4*5.1*6.4)/(4*pi))^2*9.3*(sin(45))^2.

### FAQ

What is Poynting Vector Magnitude?
Poynting Vector Magnitude represents the rate of energy flow per unit area in an electromagnetic field, calculated as the cross product of the electric and magnetic fields, measured in watts per square meter and is represented as Sr = 1/2*((Id*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?
Poynting Vector Magnitude represents the rate of energy flow per unit area in an electromagnetic field, calculated as the cross product of the electric and magnetic fields, measured in watts per square meter 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 (Id), 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.
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