Maximum Electron Current per Unit Area Calculator

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✖Emission Constant is a constant.ⓘ Emission Constant [A₁]			+10% -10%
✖Temperature is a physical quantity that describes the level of thermal energy in a system.ⓘ Temperature [T]			+10% -10%
✖Work Function is a measure of the minimum amount of energy needed to remove an electron from a solid surface and set it free.ⓘ Work Function [Φ]			+10% -10%

✖Current Density is a measure of the flow of electric charge through a given area of a conductor.ⓘ Maximum Electron Current per Unit Area [J]

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Maximum Electron Current per Unit Area

Formula

`"J" = "A"_{"1"}*"T"^2*exp(-"Φ"/("[BoltZ]"*"T"))`

Example

`"3.138127A/cm²"="120"*("1100K")^2*exp(-"0.8eV"/("[BoltZ]"*("1100K")))`

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Maximum Electron Current per Unit Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Current Density = Emission Constant*Temperature^2*exp(-Work Function/([BoltZ]*Temperature))
J = A₁*T^2*exp(-Φ/([BoltZ]*T))
This formula uses 2 Constants, 1 Functions, 4 Variables

Constants Used

[BoltZ] - Boltzmann constant Value Taken As 1.38064852E-23 Joule/Kelvin
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249

Functions Used

exp - Exponential function, exp(Number)

Variables Used

Current Density - (Measured in Ampere per Square Meter) - Current Density is a measure of the flow of electric charge through a given area of a conductor.
Emission Constant - Emission Constant is a constant.
Temperature - (Measured in Kelvin) - Temperature is a physical quantity that describes the level of thermal energy in a system.
Work Function - (Measured in Joule) - Work Function is a measure of the minimum amount of energy needed to remove an electron from a solid surface and set it free.

STEP 1: Convert Input(s) to Base Unit

Emission Constant: 120 --> No Conversion Required
Temperature: 1100 Kelvin --> 1100 Kelvin No Conversion Required
Work Function: 0.8 Electron-Volt --> 1.28174186400001E-19 Joule (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

J = A₁*T^2*exp(-Φ/([BoltZ]*T)) --> 120*1100^2*exp(-1.28174186400001E-19/([BoltZ]*1100))

Evaluating ... ...

J = 31381.2706241948

STEP 3: Convert Result to Output's Unit

31381.2706241948 Ampere per Square Meter -->3.13812706241948 Ampere per Square Centimeter (Check conversion here)

FINAL ANSWER

3.13812706241948 Ampere per Square Centimeter <-- Current Density

(Calculation completed in 00.000 seconds)

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Credits

Created by Nisarg

Indian Institute of Technology,Roorlee (IITR), Roorkee

Nisarg has created this Calculator and 100+ more calculators!

Verified by Parminder Singh

Chandigarh University (CU), Punjab

Parminder Singh has verified this Calculator and 300+ more calculators!

< 9 Thermal Power Plant Calculators

Net Rate of Energy Supply to Cathode

Go Net Energy Cathode = Cathode Current Density*(Cathode Voltage+(2*[BoltZ]*Cathode Temperature)/[Charge-e])-Anode Current Density*(Anode Voltage+(2*[BoltZ]*Anode Temperature)/[Charge-e])

Current Density from Cathode to Anode

Go Cathode Current Density = Emission Constant*Cathode Temperature^2*exp(-([Charge-e]*Cathode Voltage)/([BoltZ]*Cathode Temperature))

Maximum Electron Current per Unit Area

Go Current Density = Emission Constant*Temperature^2*exp(-Work Function/([BoltZ]*Temperature))

Net Kinetic Energy of Electron

Go Electron Net Energy = Cathode Current Density*((2*[BoltZ]*Cathode Temperature)/[Charge-e])

Output Voltage given Fermi Energy Levels

Go Output Voltage = (1/[Charge-e])*(Anode Fermi Energy Level-Cathode Fermi Energy Level)

Power Output from Generator

Go Power Output = Output Voltage*(Cathode Current Density-Anode Current Density)

Output Voltage given Anode and Cathode Work Functions

Go Output Voltage = Cathode Work Function-Anode Work Function

Minimum Energy Required by Electron to Leave Cathode

Go Net Energy = Cathode Current Density*Cathode Voltage

Output Voltage given Anode and Cathode Voltages

Go Output Voltage = Cathode Voltage-Anode Voltage

Maximum Electron Current per Unit Area Formula

Current Density = Emission Constant*Temperature^2*exp(-Work Function/([BoltZ]*Temperature))
J = A₁*T^2*exp(-Φ/([BoltZ]*T))

What is Thermionic Power Generation?

Thermionic power generation is a method of producing electricity by converting heat energy directly into electrical energy through the use of thermionic emission. It is based on the phenomenon of electrons being emitted from a heated surface or filament when it is subjected to a sufficiently high temperature.

How to Calculate Maximum Electron Current per Unit Area?

Maximum Electron Current per Unit Area calculator uses Current Density = Emission Constant*Temperature^2*exp(-Work Function/([BoltZ]*Temperature)) to calculate the Current Density, The Maximum Electron Current per Unit Area formula is defined as a measure of the flow of electric charge through a given area of a conductor. It is defined as the amount of electric current passing through a unit area perpendicular to the direction of current flow. Current Density is denoted by J symbol.

How to calculate Maximum Electron Current per Unit Area using this online calculator? To use this online calculator for Maximum Electron Current per Unit Area, enter Emission Constant (A₁), Temperature (T) & Work Function (Φ) and hit the calculate button. Here is how the Maximum Electron Current per Unit Area calculation can be explained with given input values -> 3.138127 = 120*1100^2*exp(-1.28174186400001E-19/([BoltZ]*1100)).

FAQ

What is Maximum Electron Current per Unit Area?

The Maximum Electron Current per Unit Area formula is defined as a measure of the flow of electric charge through a given area of a conductor. It is defined as the amount of electric current passing through a unit area perpendicular to the direction of current flow and is represented as J = A₁*T^2*exp(-Φ/([BoltZ]*T)) or Current Density = Emission Constant*Temperature^2*exp(-Work Function/([BoltZ]*Temperature)). Emission Constant is a constant, Temperature is a physical quantity that describes the level of thermal energy in a system & Work Function is a measure of the minimum amount of energy needed to remove an electron from a solid surface and set it free.

How to calculate Maximum Electron Current per Unit Area?

The Maximum Electron Current per Unit Area formula is defined as a measure of the flow of electric charge through a given area of a conductor. It is defined as the amount of electric current passing through a unit area perpendicular to the direction of current flow is calculated using Current Density = Emission Constant*Temperature^2*exp(-Work Function/([BoltZ]*Temperature)). To calculate Maximum Electron Current per Unit Area, you need Emission Constant (A₁), Temperature (T) & Work Function (Φ). With our tool, you need to enter the respective value for Emission Constant, Temperature & Work Function 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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