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Maximum Power Density of Half-Wave Dipole Formula

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Maximum Power Density refers to the highest amount of power per unit area that is present within a given region of space. Check FAQs

[P] max = \frac{η hwd \cdot {I o}^{2}}{4 \cdot π^{2} \cdot {r hwd}^{2}} \cdot {\sin ((((W hwd \cdot t) - (\frac{π}{L hwd}) \cdot r hwd)) \cdot \frac{π}{180})}^{2}

[P]_max - Maximum Power Density?η_hwd - Intrinsic Impedance of Medium?I_o - Amplitude of Oscillating Current?r_hwd - Radial Distance from Antenna?W_hwd - Angular Frequency of Half Wave Dipole?t - Time?L_hwd - Length of Antenna?π - Archimedes' constant?

Maximum Power Density of Half-Wave Dipole Example

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Here is how the Maximum Power Density of Half-Wave Dipole equation looks like with Values.

Here is how the Maximum Power Density of Half-Wave Dipole equation looks like with Units.

Here is how the Maximum Power Density of Half-Wave Dipole equation looks like.

120.2588 = \frac{377 \cdot 5^{2}}{4 \cdot {3.1416}^{2} \cdot {0.5}^{2}} \cdot {\sin ((((6.3E+7 \cdot 0.001) - (\frac{3.1416}{2}) \cdot 0.5)) \cdot \frac{3.1416}{180})}^{2}

120.2588W/m³ = \frac{377Ω \cdot {5A}^{2}}{4 \cdot {3.1416}^{2} \cdot {0.5m}^{2}} \cdot {\sin ((((6.3E+7rad/s \cdot 0.001s) - (\frac{3.1416}{2m}) \cdot 0.5m)) \cdot \frac{3.1416}{180})}^{2}

120.2588 = \frac{377 \cdot 5^{2}}{4 \cdot {3.1416}^{2} \cdot {0.5}^{2}} \cdot {\sin ((((6.3E+7 \cdot 0.001) - (\frac{3.1416}{2}) \cdot 0.5)) \cdot \frac{3.1416}{180})}^{2}

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Maximum Power Density of Half-Wave Dipole Solution

Follow our step by step solution on how to calculate Maximum Power Density of Half-Wave Dipole?

FIRST Step Consider the formula

[P] max = \frac{η hwd \cdot {I o}^{2}}{4 \cdot π^{2} \cdot {r hwd}^{2}} \cdot {\sin ((((W hwd \cdot t) - (\frac{π}{L hwd}) \cdot r hwd)) \cdot \frac{π}{180})}^{2}

Next Step Substitute values of Variables

∴

[P] max = \frac{377Ω \cdot {5A}^{2}}{4 \cdot π^{2} \cdot {0.5m}^{2}} \cdot {\sin ((((6.3E+7rad/s \cdot 0.001s) - (\frac{π}{2m}) \cdot 0.5m)) \cdot \frac{π}{180})}^{2}

Next Step Substitute values of Constants

∴

[P] max = \frac{377Ω \cdot {5A}^{2}}{4 \cdot {3.1416}^{2} \cdot {0.5m}^{2}} \cdot {\sin ((((6.3E+7rad/s \cdot 0.001s) - (\frac{3.1416}{2m}) \cdot 0.5m)) \cdot \frac{3.1416}{180})}^{2}

Next Step Prepare to Evaluate

∴

[P] max = \frac{377 \cdot 5^{2}}{4 \cdot {3.1416}^{2} \cdot {0.5}^{2}} \cdot {\sin ((((6.3E+7 \cdot 0.001) - (\frac{3.1416}{2}) \cdot 0.5)) \cdot \frac{3.1416}{180})}^{2}

Next Step Evaluate

∴

[P] max = 120.25884547098W/m³

LAST Step Rounding Answer

∴

[P] max = 120.2588W/m³

Maximum Power Density of Half-Wave Dipole Formula Elements

Variables

Constants

Functions

Maximum Power Density

Maximum Power Density refers to the highest amount of power per unit area that is present within a given region of space.

Symbol: [P]_max

Measurement: Power DensityUnit: W/m³

Note: Value should be greater than 0.

Formulas to find Maximum Power Density

Intrinsic Impedance of Medium

The Intrinsic Impedance of Medium refers to the characteristic impedance of a material through which electromagnetic waves propagate.

Symbol: η_hwd

Measurement: Electric ResistanceUnit: Ω

Note: Value should be greater than 0.

Formulas to find Intrinsic Impedance of Medium

Amplitude of Oscillating Current

The Amplitude of Oscillating Current refers to the maximum magnitude or strength of the alternating electric current as it varies over time.

Symbol: I_o

Measurement: Electric CurrentUnit: A

Note: Value should be greater than 0.

Formulas to find Amplitude of Oscillating Current

Radial Distance from Antenna

The Radial Distance from Antenna refers to the distance measured radially outward from the center of the antenna structure.

Symbol: r_hwd

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radial Distance from Antenna

Angular Frequency of Half Wave Dipole

The Angular Frequency of Half Wave Dipole refers to the rate at which the dipole oscillates back and forth in an electromagnetic field.

Symbol: W_hwd

Measurement: Angular FrequencyUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Angular Frequency of Half Wave Dipole

Time

Time is a dimension in which events occur in succession, allowing for the measurement of durations between those events.

Symbol: t

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Time

Length of Antenna

The Length of Antenna refers to the physical size of the conductive element that make up the antenna structure.

Symbol: L_hwd

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Antenna

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

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

Maximum Power Density of Half-Wave Dipole evaluator 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 evaluate the Maximum Power Density, Maximum Power Density of Half-Wave Dipole is the highest radiated power per unit area, occurring in the direction perpendicular to the dipole, typically measured in the far field. Maximum Power Density is denoted by [P]_max symbol.

How to evaluate Maximum Power Density of Half-Wave Dipole using this online evaluator? To use this online evaluator for Maximum 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.

FAQs on Maximum Power Density of Half-Wave Dipole

What is the formula to find Maximum Power Density of Half-Wave Dipole?

The formula of Maximum Power Density of Half-Wave Dipole is expressed as 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. Here is an example- 120.2588 = (377*5^2)/(4*pi^2*0.5^2)*sin((((62800000*0.001)-(pi/2)*0.5))*pi/180)^2.

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

With 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) we can find Maximum Power Density of Half-Wave Dipole using the 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. This formula also uses Archimedes' constant and Sine (sin) function(s).

Can the Maximum Power Density of Half-Wave Dipole be negative?

No, the Maximum Power Density of Half-Wave Dipole, measured in Power Density cannot be negative.

Which unit is used to measure Maximum Power Density of Half-Wave Dipole?

Maximum Power Density of Half-Wave Dipole is usually measured using the Watt Per Cubic Meter[W/m³] for Power Density. Horsepower Per Litre[W/m³], Decawatt Per Cubic Meter[W/m³], Gigawatt Per Cubic Meter[W/m³] are the few other units in which Maximum Power Density of Half-Wave Dipole can be measured.

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Maximum Power Density of Half-Wave Dipole Formula

Maximum Power Density of Half-Wave Dipole Example

Maximum Power Density of Half-Wave Dipole Solution

Maximum Power Density of Half-Wave Dipole Formula Elements

Other formulas in Electromagnetic Radiation and Antennas category

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

FAQs on Maximum Power Density of Half-Wave Dipole

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