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Poynting Vector Magnitude Formula

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Poynting Vector is a vector quantity that describes the directional energy flux density of an electromagnetic field. Check FAQs

S r = \frac{1}{2} \cdot {(\frac{I d \cdot k \cdot d}{4 \cdot π})}^{2} \cdot η \cdot {(\sin (θ))}^{2}

S_r - Poynting Vector?I_d - Dipole Current?k - Wavenumber?d - Source Distance?η - Intrinsic Impedance?θ - Polar Angle?π - Archimedes' constant?

Poynting Vector Magnitude Example

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Here is how the Poynting Vector Magnitude equation looks like with Values.

Here is how the Poynting Vector Magnitude equation looks like with Units.

Here is how the Poynting Vector Magnitude equation looks like.

12.4373 = \frac{1}{2} \cdot {(\frac{23.4 \cdot 5.1 \cdot 6.4}{4 \cdot 3.1416})}^{2} \cdot 9.3 \cdot {(\sin (45))}^{2}

12.4373kW/m² = \frac{1}{2} \cdot {(\frac{23.4A \cdot 5.1 \cdot 6.4m}{4 \cdot 3.1416})}^{2} \cdot 9.3Ω \cdot {(\sin (45rad))}^{2}

12.4373 = \frac{1}{2} \cdot {(\frac{23.4 \cdot 5.1 \cdot 6.4}{4 \cdot 3.1416})}^{2} \cdot 9.3 \cdot {(\sin (45))}^{2}

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Poynting Vector Magnitude Solution

Follow our step by step solution on how to calculate Poynting Vector Magnitude?

FIRST Step Consider the formula

S r = \frac{1}{2} \cdot {(\frac{I d \cdot k \cdot d}{4 \cdot π})}^{2} \cdot η \cdot {(\sin (θ))}^{2}

Next Step Substitute values of Variables

∴

S r = \frac{1}{2} \cdot {(\frac{23.4A \cdot 5.1 \cdot 6.4m}{4 \cdot π})}^{2} \cdot 9.3Ω \cdot {(\sin (45rad))}^{2}

Next Step Substitute values of Constants

∴

S r = \frac{1}{2} \cdot {(\frac{23.4A \cdot 5.1 \cdot 6.4m}{4 \cdot 3.1416})}^{2} \cdot 9.3Ω \cdot {(\sin (45rad))}^{2}

Next Step Prepare to Evaluate

∴

S r = \frac{1}{2} \cdot {(\frac{23.4 \cdot 5.1 \cdot 6.4}{4 \cdot 3.1416})}^{2} \cdot 9.3 \cdot {(\sin (45))}^{2}

Next Step Evaluate

∴

S r = 12437.2935528007W/m²

Next Step Convert to Output's Unit

∴

S r = 12.4372935528007kW/m²

LAST Step Rounding Answer

∴

S r = 12.4373kW/m²

Poynting Vector Magnitude Formula Elements

Variables

Constants

Functions

Poynting Vector

Poynting Vector is a vector quantity that describes the directional energy flux density of an electromagnetic field.

Symbol: S_r

Measurement: Heat Flux DensityUnit: kW/m²

Note: Value should be greater than 0.

Formulas to find Poynting Vector

Dipole Current

Dipole Current is the current flowing through a hertzian dipole antenna.

Symbol: I_d

Measurement: Electric CurrentUnit: A

Note: Value should be greater than 0.

Formulas to find Dipole Current

Wavenumber

Wavenumber represents the spatial frequency of a wave, signifying how many times the wave pattern repeats within a specific unit distance.

Symbol: k

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Wavenumber

Source Distance

Source Distance represents the distance from the point of observation to the source of the wave.

Symbol: d

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Source Distance

Intrinsic Impedance

Intrinsic Impedance is a property of a medium that represents the resistance it offers to the propagation of electromagnetic waves.

Symbol: η

Measurement: Electric ResistanceUnit: Ω

Note: Value should be greater than 0.

Formulas to find Intrinsic Impedance

Polar Angle

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.

Symbol: θ

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Polar Angle

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sin(Angle)

Other formulas in Electromagnetic Radiation and Antennas category

Go Radiation Resistance of Antenna

R rad = 2 \cdot \frac{P r}{{i o}^{2}}

Go Average Power

P r = \frac{1}{2} \cdot {i o}^{2} \cdot R rad

Go Radiation Efficiency of Antenna

η r = \frac{G}{D max}

Go Magnetic Field for Hertzian Dipole

H Φ = {(\frac{1}{r})}^{2} \cdot (\cos (2 \cdot π \cdot \frac{r}{λ}) + 2 \cdot π \cdot \frac{r}{λ} \cdot \sin (2 \cdot π \cdot \frac{r}{λ}))

How to Evaluate Poynting Vector Magnitude?

Poynting Vector Magnitude evaluator uses Poynting Vector = 1/2*((Dipole Current*Wavenumber*Source Distance)/(4*pi))^2*Intrinsic Impedance*(sin(Polar Angle))^2 to evaluate 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 S_r symbol.

How to evaluate Poynting Vector Magnitude using this online evaluator? To use this online evaluator 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.

FAQs on Poynting Vector Magnitude

What is the formula to find Poynting Vector Magnitude?

The formula of Poynting Vector Magnitude is expressed as Poynting Vector = 1/2*((Dipole Current*Wavenumber*Source Distance)/(4*pi))^2*Intrinsic Impedance*(sin(Polar Angle))^2. Here is an example- 12437.29 = 1/2*((23.4*5.1*6.4)/(4*pi))^2*9.3*(sin(45))^2.

How to calculate Poynting Vector Magnitude?

With Dipole Current (I_d), Wavenumber (k), Source Distance (d), Intrinsic Impedance (η) & Polar Angle (θ) we can find Poynting Vector Magnitude using the formula - Poynting Vector = 1/2*((Dipole Current*Wavenumber*Source Distance)/(4*pi))^2*Intrinsic Impedance*(sin(Polar Angle))^2. This formula also uses Archimedes' constant and Sine (sin) function(s).

Can the Poynting Vector Magnitude be negative?

No, the Poynting Vector Magnitude, measured in Heat Flux Density cannot be negative.

Which unit is used to measure Poynting Vector Magnitude?

Poynting Vector Magnitude is usually measured using the Kilowatt per Square Meter[kW/m²] for Heat Flux Density. Watt per Square Meter[kW/m²], Watt per Square Centimeter[kW/m²], Watt per Square Inch[kW/m²] are the few other units in which Poynting Vector Magnitude can be measured.

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Poynting Vector Magnitude Formula

Poynting Vector Magnitude Example

Poynting Vector Magnitude Solution

Poynting Vector Magnitude Formula Elements

Other formulas in Electromagnetic Radiation and Antennas category

How to Evaluate Poynting Vector Magnitude?

FAQs on Poynting Vector Magnitude

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