Power that Crosses Surface of Sphere Solution

STEP 0: Pre-Calculation Summary
Formula Used
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))
Psphere = pi*((Io*k*L)/(4*pi))^2*ηhwd*(int(sin(θem)^3*x,x,0,pi))
This formula uses 1 Constants, 2 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)
int - The definite integral can be used to calculate net signed area, which is the area above the x -axis minus the area below the x -axis., int(expr, arg, from, to)
Variables Used
Power Crossed at Sphere Surface - (Measured in Watt) - Power Crossed at Sphere Surface time-averaged power that crosses the surface of a sphere centered at the antenna.
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.
Wavenumber - Wavenumber represents the spatial frequency of a wave, signifying how many times the wave pattern repeats within a specific unit distance.
Short Antenna Length - (Measured in Meter) - Short Antenna Length represents the length of the short antenna with a uniform current distribution.
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.
Theta - (Measured in Radian) - Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.
STEP 1: Convert Input(s) to Base Unit
Amplitude of Oscillating Current: 5 Ampere --> 5 Ampere No Conversion Required
Wavenumber: 5 --> No Conversion Required
Short Antenna Length: 3.69 Meter --> 3.69 Meter No Conversion Required
Intrinsic Impedance of Medium: 377 Ohm --> 377 Ohm No Conversion Required
Theta: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Psphere = pi*((Io*k*L)/(4*pi))^2*ηhwd*(int(sin(θem)^3*x,x,0,pi)) --> pi*((5*5*3.69)/(4*pi))^2*377*(int(sin(0.5235987755982)^3*x,x,0,pi))
Evaluating ... ...
Psphere = 39371.6854941775
STEP 3: Convert Result to Output's Unit
39371.6854941775 Watt --> No Conversion Required
FINAL ANSWER
39371.6854941775 39371.69 Watt <-- Power Crossed at Sphere Surface
(Calculation completed in 00.004 seconds)

Credits

Created by Vignesh Naidu
Vellore Institute of Technology (VIT), Vellore,Tamil Nadu
Vignesh Naidu has created this Calculator and 25+ more calculators!
Verified by Dipanjona Mallick
Heritage Insitute of technology (HITK), Kolkata
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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

Power that Crosses Surface of Sphere Formula

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))
Psphere = pi*((Io*k*L)/(4*pi))^2*ηhwd*(int(sin(θem)^3*x,x,0,pi))

What are the Applications of Power that Crosses the Surface of Sphere ?

1. Antenna Theory: It helps calculate the power radiated by an antenna system into the surrounding environment. By integrating over the entire sphere, we can determine the total power output of the antenna.
2. Electromagnetic Wave Propagation: It can be used to analyze the propagation characteristics of electromagnetic waves in different media. By studying the power density distribution, we can understand how the wave intensity varies with distance and direction.
3. Microwave Engineering: It is relevant in designing microwave devices like waveguides and cavities. The power density distribution helps optimize the performance of these devices.

How to Calculate Power that Crosses Surface of Sphere?

Power that Crosses Surface of Sphere calculator uses 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)) to calculate the Power Crossed at Sphere Surface, The Power that Crosses Surface of Sphere formula relates the time-averaged power density to the time-average Poynting vector across the surface of a sphere with radius r centered at the antenna. Power Crossed at Sphere Surface is denoted by Psphere symbol.

How to calculate Power that Crosses Surface of Sphere using this online calculator? To use this online calculator for Power that Crosses Surface of Sphere, enter Amplitude of Oscillating Current (Io), Wavenumber (k), Short Antenna Length (L), Intrinsic Impedance of Medium hwd) & Theta em) and hit the calculate button. Here is how the Power that Crosses Surface of Sphere calculation can be explained with given input values -> 39371.69 = pi*((5*5*3.69)/(4*pi))^2*377*(int(sin(0.5235987755982)^3*x,x,0,pi)).

FAQ

What is Power that Crosses Surface of Sphere?
The Power that Crosses Surface of Sphere formula relates the time-averaged power density to the time-average Poynting vector across the surface of a sphere with radius r centered at the antenna and is represented as Psphere = pi*((Io*k*L)/(4*pi))^2*ηhwd*(int(sin(θem)^3*x,x,0,pi)) or 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)). The Amplitude of Oscillating Current refers to the maximum magnitude or strength of the alternating electric current as it varies over time, Wavenumber represents the spatial frequency of a wave, signifying how many times the wave pattern repeats within a specific unit distance, Short Antenna Length represents the length of the short antenna with a uniform current distribution, The Intrinsic Impedance of Medium, refers to the characteristic impedance of a material through which electromagnetic waves propagate & Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.
How to calculate Power that Crosses Surface of Sphere?
The Power that Crosses Surface of Sphere formula relates the time-averaged power density to the time-average Poynting vector across the surface of a sphere with radius r centered at the antenna is calculated using 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)). To calculate Power that Crosses Surface of Sphere, you need Amplitude of Oscillating Current (Io), Wavenumber (k), Short Antenna Length (L), Intrinsic Impedance of Medium hwd) & Theta em). With our tool, you need to enter the respective value for Amplitude of Oscillating Current, Wavenumber, Short Antenna Length, Intrinsic Impedance of Medium & Theta 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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