Maximum Power Density of Half-Wave Dipole Solution

STEP 0: Pre-Calculation Summary
Formula Used
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
[P]max = (ηhwd*Io^2)/(4*pi^2*rhwd^2)*sin((((Whwd*t)-(pi/Lhwd)*rhwd))*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 - Trigonometric sine function, sin(Angle)
Variables Used
Maximum Power Density - (Measured in Watt Per Cubic Meter) - Maximum Power Density refers to the highest amount of power per unit area that is present within a given region of space.
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
[P]max = (ηhwd*Io^2)/(4*pi^2*rhwd^2)*sin((((Whwd*t)-(pi/Lhwd)*rhwd))*pi/180)^2 --> (377*5^2)/(4*pi^2*0.5^2)*sin((((62800000*0.001)-(pi/2)*0.5))*pi/180)^2
Evaluating ... ...
[P]max = 120.25884547098
STEP 3: Convert Result to Output's Unit
120.25884547098 Watt Per Cubic Meter --> No Conversion Required
FINAL ANSWER
120.25884547098 120.2588 Watt Per Cubic Meter <-- Maximum Power Density
(Calculation completed in 00.004 seconds)

Credits

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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13 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
Poynting Vector Magnitude
Go Poynting Vector = 1/2*((Dipole Current*Wavenumber*Source Distance)/ (4*pi))^2*Intrinsic Impedance*(sin(Polar Angle))^2
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

Maximum Power Density of Half-Wave Dipole Formula

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
[P]max = (ηhwd*Io^2)/(4*pi^2*rhwd^2)*sin((((Whwd*t)-(pi/Lhwd)*rhwd))*pi/180)^2

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

The highest power density of a half-wave dipole antenna is very important for public health safety as well as communication technology. It establishes the radiation intensity in the area surrounding the antenna as a measure of the concentration of electromagnetic energy. It is essential to comprehend and control this power density in order to maximize communication system efficiency, guarantee effective signal transmission, and preserve dependable connectivity. In addition, determining the maximum power density is crucial to assessing the possible health concerns linked to electromagnetic radiation exposure. We can utilize the advantages of wireless communication technologies while minimizing any negative impacts on human health by abiding by safety regulations and standards that set exposure limits.

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

Maximum Power Density of Half-Wave Dipole calculator uses 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 to calculate the Maximum Power Density, The Maximum Power Density of Half-Wave Dipole antenna refers to the highest power per unit area that is radiated away from the antenna and distributed in the surrounding space. It represents the concentration of electromagnetic energy in the vicinity of the antenna. Maximum Power Density is denoted by [P]max symbol.

How to calculate Maximum Power Density of Half-Wave Dipole using this online calculator? To use this online calculator for Maximum Power Density of Half-Wave Dipole, enter Intrinsic Impedance of Medium hwd), Amplitude of Oscillating Current (Io), Radial Distance From Antenna (rhwd), Angular Frequency of Half Wave Dipole (Whwd), Time (t) & Length of Antenna (Lhwd) and hit the calculate button. Here is how the Maximum Power Density of Half-Wave Dipole calculation can be explained with given input values -> 120.2588 = (377*5^2)/(4*pi^2*0.5^2)*sin((((62800000*0.001)-(pi/2)*0.5))*pi/180)^2.

FAQ

What is Maximum Power Density of Half-Wave Dipole?
The Maximum Power Density of Half-Wave Dipole antenna refers to the highest power per unit area that is radiated away from the antenna and distributed in the surrounding space. It represents the concentration of electromagnetic energy in the vicinity of the antenna and is represented as [P]max = (ηhwd*Io^2)/(4*pi^2*rhwd^2)*sin((((Whwd*t)-(pi/Lhwd)*rhwd))*pi/180)^2 or 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. 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 Maximum Power Density of Half-Wave Dipole?
The Maximum Power Density of Half-Wave Dipole antenna refers to the highest power per unit area that is radiated away from the antenna and distributed in the surrounding space. It represents the concentration of electromagnetic energy in the vicinity of the antenna is calculated using 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. To calculate Maximum Power Density of Half-Wave Dipole, you need Intrinsic Impedance of Medium hwd), Amplitude of Oscillating Current (Io), Radial Distance From Antenna (rhwd), Angular Frequency of Half Wave Dipole (Whwd), Time (t) & Length of Antenna (Lhwd). 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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