Magnetic Field for Hertzian Dipole Calculator

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✖Dipole Distance refers to the radial distance from the dipole.ⓘ Dipole Distance [r]			+10% -10%
✖Wavelength of Dipole refers to the wavelength of radiation emitted by the dipole.ⓘ Wavelength of Dipole [λ]			+10% -10%

✖Magnetic Field Component refers to the azimuthal component of the magnetic field.ⓘ Magnetic Field for Hertzian Dipole [H_Φ]

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Formula

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Magnetic Field for Hertzian Dipole

Formula

`"H"_{"Φ"} = (1/"r")^2*(cos(2*pi*"r"/"λ")+2*pi*"r"/"λ"*sin(2*pi*"r"/"λ"))`

Example

`"0.006773A/m"=(1/"8.3m")^2*(cos(2*pi*"8.3m"/"20m")+2*pi*"8.3m"/"20m"*sin(2*pi*"8.3m"/"20m"))`

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Magnetic Field for Hertzian Dipole Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
H_Φ = (1/r)^2*(cos(2*pi*r/λ)+2*pi*r/λ*sin(2*pi*r/λ))
This formula uses 1 Constants, 2 Functions, 3 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)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Magnetic Field Component - (Measured in Ampere per Meter) - Magnetic Field Component refers to the azimuthal component of the magnetic field.
Dipole Distance - (Measured in Meter) - Dipole Distance refers to the radial distance from the dipole.
Wavelength of Dipole - (Measured in Meter) - Wavelength of Dipole refers to the wavelength of radiation emitted by the dipole.

STEP 1: Convert Input(s) to Base Unit

Dipole Distance: 8.3 Meter --> 8.3 Meter No Conversion Required
Wavelength of Dipole: 20 Meter --> 20 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

H_Φ = (1/r)^2*(cos(2*pi*r/λ)+2*pi*r/λ*sin(2*pi*r/λ)) --> (1/8.3)^2*(cos(2*pi*8.3/20)+2*pi*8.3/20*sin(2*pi*8.3/20))

Evaluating ... ...

H_Φ = 0.00677303837762137

STEP 3: Convert Result to Output's Unit

0.00677303837762137 Ampere per Meter --> No Conversion Required

FINAL ANSWER

0.00677303837762137 ≈ 0.006773 Ampere per Meter <-- Magnetic Field Component

(Calculation completed in 00.004 seconds)

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Created by Gowthaman N

Vellore Institute of Technology (VIT University), Chennai

Gowthaman N has created this Calculator and 25+ more calculators!

Verified by Ritwik Tripathi

Vellore Institute of Technology (VIT Vellore), Vellore

Ritwik Tripathi has verified this Calculator and 100+ more calculators!

< 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

Magnetic Field for Hertzian Dipole Formula

What field ratio dominates near a Hertzian dipole?

The dipole term, 1/r², dominates in the near field because it decreases more rapidly with distance (proportionally to 1/r²) compared to the radiation term, which decreases only proportionally to 1/r.

How to Calculate Magnetic Field for Hertzian Dipole?

Magnetic Field for Hertzian Dipole calculator uses 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)) to calculate the Magnetic Field Component, The Magnetic Field for Hertzian Dipole represents the azimuthal component of the magnetic field generated by a Hertzian dipole in the far field.It describes how the magnetic field varies with distance and wavelength in a cylindrical coordinate system. Magnetic Field Component is denoted by H_Φ symbol.

How to calculate Magnetic Field for Hertzian Dipole using this online calculator? To use this online calculator for Magnetic Field for Hertzian Dipole, enter Dipole Distance (r) & Wavelength of Dipole (λ) and hit the calculate button. Here is how the Magnetic Field for Hertzian Dipole calculation can be explained with given input values -> -0.150204 = (1/8.3)^2*(cos(2*pi*8.3/20)+2*pi*8.3/20*sin(2*pi*8.3/20)).

FAQ

What is Magnetic Field for Hertzian Dipole?

The Magnetic Field for Hertzian Dipole represents the azimuthal component of the magnetic field generated by a Hertzian dipole in the far field.It describes how the magnetic field varies with distance and wavelength in a cylindrical coordinate system and is represented as H_Φ = (1/r)^2*(cos(2*pi*r/λ)+2*pi*r/λ*sin(2*pi*r/λ)) or 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)). Dipole Distance refers to the radial distance from the dipole & Wavelength of Dipole refers to the wavelength of radiation emitted by the dipole.

How to calculate Magnetic Field for Hertzian Dipole?

The Magnetic Field for Hertzian Dipole represents the azimuthal component of the magnetic field generated by a Hertzian dipole in the far field.It describes how the magnetic field varies with distance and wavelength in a cylindrical coordinate system is calculated using 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)). To calculate Magnetic Field for Hertzian Dipole, you need Dipole Distance (r) & Wavelength of Dipole (λ). With our tool, you need to enter the respective value for Dipole Distance & Wavelength of Dipole 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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