Average Power Density of Half-Wave Dipole Calculator

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✖The Intrinsic Impedance of Medium, refers to the characteristic impedance of a material through which electromagnetic waves propagate.ⓘ Intrinsic Impedance of Medium [η_hwd]			+10% -10%
✖The Amplitude of Oscillating Current refers to the maximum magnitude or strength of the alternating electric current as it varies over time.ⓘ Amplitude of Oscillating Current [I_o]			+10% -10%
✖The Radial Distance From Antenna refers to the distance measured radially outward from the center of the antenna structure.ⓘ Radial Distance From Antenna [r_hwd]			+10% -10%
✖The Angular Frequency of Half Wave Dipole refers to the rate at which the dipole oscillates back and forth in an electromagnetic field.ⓘ Angular Frequency of Half Wave Dipole [W_hwd]			+10% -10%
✖Time is a dimension in which events occur in succession, allowing for the measurement of durations between those events.ⓘ Time [t]			+10% -10%
✖The Length of Antenna refers to the physical size of the conductive element that make up the antenna structure.ⓘ Length of Antenna [L_hwd]			+10% -10%

✖Average Power Density refers to the average amount of power per unit area that is present within a given region of space over a specified period of time.ⓘ Average Power Density of Half-Wave Dipole [[Pr]_avg]

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Formula

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Average Power Density of Half-Wave Dipole

Formula

`"[Pr]"_{"avg"} = (0.609*"η"_{"hwd"}*"I"_{"o"}^2)/(4*pi^2*"r"_{"hwd"}^2)*sin(((("W"_{"hwd"}*"t")-(pi/"L"_{"hwd"})*"r"_{"hwd"}))*pi/180)^2`

Example

`"73.23764W/m³"=(0.609*"377Ω"*("5A")^2)/(4*pi^2*("0.5m")^2)*sin(((("6.28e7rad/s"*"0.001s")-(pi/"2m")*"0.5m"))*pi/180)^2`

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Average Power Density of Half-Wave Dipole Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
[Pr]_avg = (0.609*η_hwd*I_o^2)/(4*pi^2*r_hwd^2)*sin((((W_hwd*t)-(pi/L_hwd)*r_hwd))*pi/180)^2
This formula uses 1 Constants, 1 Functions, 7 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

Average Power Density - (Measured in Watt Per Cubic Meter) - Average Power Density refers to the average amount of power per unit area that is present within a given region of space over a specified period of time.
Intrinsic Impedance of Medium - (Measured in Ohm) - The Intrinsic Impedance of Medium, refers to the characteristic impedance of a material through which electromagnetic waves propagate.
Amplitude of Oscillating Current - (Measured in Ampere) - The Amplitude of Oscillating Current refers to the maximum magnitude or strength of the alternating electric current as it varies over time.
Radial Distance From Antenna - (Measured in Meter) - The Radial Distance From Antenna refers to the distance measured radially outward from the center of the antenna structure.
Angular Frequency of Half Wave Dipole - (Measured in Radian per Second) - The Angular Frequency of Half Wave Dipole refers to the rate at which the dipole oscillates back and forth in an electromagnetic field.
Time - (Measured in Second) - Time is a dimension in which events occur in succession, allowing for the measurement of durations between those events.
Length of Antenna - (Measured in Meter) - The Length of Antenna refers to the physical size of the conductive element that make up the antenna structure.

STEP 1: Convert Input(s) to Base Unit

Intrinsic Impedance of Medium: 377 Ohm --> 377 Ohm No Conversion Required
Amplitude of Oscillating Current: 5 Ampere --> 5 Ampere No Conversion Required
Radial Distance From Antenna: 0.5 Meter --> 0.5 Meter No Conversion Required
Angular Frequency of Half Wave Dipole: 62800000 Radian per Second --> 62800000 Radian per Second No Conversion Required
Time: 0.001 Second --> 0.001 Second No Conversion Required
Length of Antenna: 2 Meter --> 2 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

[Pr]_avg = (0.609*η_hwd*I_o^2)/(4*pi^2*r_hwd^2)*sin((((W_hwd*t)-(pi/L_hwd)*r_hwd))*pi/180)^2 --> (0.609*377*5^2)/(4*pi^2*0.5^2)*sin((((62800000*0.001)-(pi/2)*0.5))*pi/180)^2

Evaluating ... ...

[Pr]_avg = 73.2376368918267

STEP 3: Convert Result to Output's Unit

73.2376368918267 Watt Per Cubic Meter --> No Conversion Required

FINAL ANSWER

73.2376368918267 ≈ 73.23764 Watt Per Cubic Meter <-- Average Power Density

(Calculation completed in 00.020 seconds)

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Created by Souradeep Dey

National Institute of Technology Agartala (NITA), Agartala, Tripura

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Dayananda Sagar College Of Engineering (DSCE), Banglore

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< 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

Average Power Density of Half-Wave Dipole Formula

What is the significance of average power density of Half-wave dipole?

The average power density of a half-wave dipole antenna is important because it plays a crucial part in figuring out how much electromagnetic radiation is present in the area around it overall. Measured as the average concentration of electromagnetic radiation per unit area over time, it offers important information about the amounts of long-term exposure that sensitive electronic equipment and humans experience. Comprehending the average power density is crucial in evaluating adherence to safety protocols and guidelines that regulate exposure to electromagnetic radiation. It is possible to reduce the probable health concerns associated with prolonged exposure to electromagnetic fields by tracking and regulating the average power density.

How to Calculate Average Power Density of Half-Wave Dipole?

Average Power Density of Half-Wave Dipole calculator uses 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 to calculate the Average Power Density, The Average Power Density of Half-Wave Dipole antenna represents the average concentration of electromagnetic energy per unit area in its vicinity over time. It's crucial for assessing long-term exposure to radiation and ensuring compliance with safety standards. Average Power Density is denoted by [Pr]_avg symbol.

How to calculate Average Power Density of Half-Wave Dipole using this online calculator? To use this online calculator for Average Power Density of Half-Wave Dipole, enter Intrinsic Impedance of Medium (η_hwd), Amplitude of Oscillating Current (I_o), Radial Distance From Antenna (r_hwd), Angular Frequency of Half Wave Dipole (W_hwd), Time (t) & Length of Antenna (L_hwd) and hit the calculate button. Here is how the Average Power Density of Half-Wave Dipole calculation can be explained with given input values -> 73.23764 = (0.609*377*5^2)/(4*pi^2*0.5^2)*sin((((62800000*0.001)-(pi/2)*0.5))*pi/180)^2.

FAQ

What is Average Power Density of Half-Wave Dipole?

The Average Power Density of Half-Wave Dipole antenna represents the average concentration of electromagnetic energy per unit area in its vicinity over time. It's crucial for assessing long-term exposure to radiation and ensuring compliance with safety standards and is represented as [Pr]_avg = (0.609*η_hwd*I_o^2)/(4*pi^2*r_hwd^2)*sin((((W_hwd*t)-(pi/L_hwd)*r_hwd))*pi/180)^2 or 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. The Intrinsic Impedance of Medium, refers to the characteristic impedance of a material through which electromagnetic waves propagate, The Amplitude of Oscillating Current refers to the maximum magnitude or strength of the alternating electric current as it varies over time, The Radial Distance From Antenna refers to the distance measured radially outward from the center of the antenna structure, The Angular Frequency of Half Wave Dipole refers to the rate at which the dipole oscillates back and forth in an electromagnetic field, Time is a dimension in which events occur in succession, allowing for the measurement of durations between those events & The Length of Antenna refers to the physical size of the conductive element that make up the antenna structure.

How to calculate Average Power Density of Half-Wave Dipole?

The Average Power Density of Half-Wave Dipole antenna represents the average concentration of electromagnetic energy per unit area in its vicinity over time. It's crucial for assessing long-term exposure to radiation and ensuring compliance with safety standards is calculated using 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. To calculate Average Power Density of Half-Wave Dipole, you need Intrinsic Impedance of Medium (η_hwd), Amplitude of Oscillating Current (I_o), Radial Distance From Antenna (r_hwd), Angular Frequency of Half Wave Dipole (W_hwd), Time (t) & Length of Antenna (L_hwd). With our tool, you need to enter the respective value for Intrinsic Impedance of Medium, Amplitude of Oscillating Current, Radial Distance From Antenna, Angular Frequency of Half Wave Dipole, Time & Length of Antenna 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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