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Repeller Voltage Formula

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Repeller Voltage refers to the voltage applied to a repeller electrode in a vacuum tube. The repeller voltage is typically negative with respect to the cathode voltage. Check FAQs

V r = \sqrt{\frac{8 \cdot ω^{2} \cdot {L ds}^{2} \cdot V o}{{((2 \cdot π \cdot M) - (\frac{π}{2}))}^{2}} \cdot (\frac{[Mass-e]}{[Charge-e]})} - V o

V_r - Repeller Voltage?ω - Angular Frequency?L_ds - Drift Space Length?V_o - Small Beam Voltage?M - Number of Oscillation?[Mass-e] - Mass of electron?[Charge-e] - Charge of electron?π - Archimedes' constant?

Repeller Voltage Example

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Here is how the Repeller Voltage equation looks like with Values.

Here is how the Repeller Voltage equation looks like with Units.

Here is how the Repeller Voltage equation looks like.

58444.6133 = \sqrt{\frac{8 \cdot {7.9E+8}^{2} \cdot {71.7}^{2} \cdot 13}{{((2 \cdot 3.1416 \cdot 4) - (\frac{3.1416}{2}))}^{2}} \cdot (\frac{9.1E-31}{1.6E-19})} - 13

58444.6133V = \sqrt{\frac{8 \cdot {7.9E+8rad/s}^{2} \cdot {71.7m}^{2} \cdot 13V}{{((2 \cdot 3.1416 \cdot 4) - (\frac{3.1416}{2}))}^{2}} \cdot (\frac{9.1E-31kg}{1.6E-19C})} - 13V

58444.6133 = \sqrt{\frac{8 \cdot {7.9E+8}^{2} \cdot {71.7}^{2} \cdot 13}{{((2 \cdot 3.1416 \cdot 4) - (\frac{3.1416}{2}))}^{2}} \cdot (\frac{9.1E-31}{1.6E-19})} - 13

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Repeller Voltage Solution

Follow our step by step solution on how to calculate Repeller Voltage?

FIRST Step Consider the formula

V r = \sqrt{\frac{8 \cdot ω^{2} \cdot {L ds}^{2} \cdot V o}{{((2 \cdot π \cdot M) - (\frac{π}{2}))}^{2}} \cdot (\frac{[Mass-e]}{[Charge-e]})} - V o

Next Step Substitute values of Variables

∴

V r = \sqrt{\frac{8 \cdot {7.9E+8rad/s}^{2} \cdot {71.7m}^{2} \cdot 13V}{{((2 \cdot π \cdot 4) - (\frac{π}{2}))}^{2}} \cdot (\frac{[Mass-e]}{[Charge-e]})} - 13V

Next Step Substitute values of Constants

∴

V r = \sqrt{\frac{8 \cdot {7.9E+8rad/s}^{2} \cdot {71.7m}^{2} \cdot 13V}{{((2 \cdot 3.1416 \cdot 4) - (\frac{3.1416}{2}))}^{2}} \cdot (\frac{9.1E-31kg}{1.6E-19C})} - 13V

Next Step Prepare to Evaluate

∴

V r = \sqrt{\frac{8 \cdot {7.9E+8}^{2} \cdot {71.7}^{2} \cdot 13}{{((2 \cdot 3.1416 \cdot 4) - (\frac{3.1416}{2}))}^{2}} \cdot (\frac{9.1E-31}{1.6E-19})} - 13

Next Step Evaluate

∴

V r = 58444.6132901852V

LAST Step Rounding Answer

∴

V r = 58444.6133V

Repeller Voltage Formula Elements

Variables

Constants

Functions

Repeller Voltage

Repeller Voltage refers to the voltage applied to a repeller electrode in a vacuum tube. The repeller voltage is typically negative with respect to the cathode voltage.

Symbol: V_r

Measurement: Electric PotentialUnit: V

Note: Value should be greater than 0.

Formulas to find Repeller Voltage

Angular Frequency

Angular Frequency of a steadily recurring phenomenon expressed in radians per second.

Symbol: ω

Measurement: Angular FrequencyUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Angular Frequency

Drift Space Length

Drift Space Length refers to the distance between two consecutive bunches of charged particles in a particle accelerator or a beam transport system.

Symbol: L_ds

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Drift Space Length

Small Beam Voltage

Small Beam Voltage is the voltage applied to an electron beam in a vacuum tube or other electronic device to accelerate the electrons and control their speed and energy.

Symbol: V_o

Measurement: Electric PotentialUnit: V

Note: Value should be greater than 0.

Formulas to find Small Beam Voltage

Number of Oscillation

Number of Oscillation refers to the occurrence of the oscillation.

Symbol: M

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Oscillation

Mass of electron

Mass of electron is a fundamental physical constant, representing the amount of matter contained within an electron, an elementary particle with a negative electric charge.

Symbol: [Mass-e]

Value: 9.10938356E-31 kg

Charge of electron

Charge of electron is a fundamental physical constant, representing the electric charge carried by an electron, which is the elementary particle with a negative electric charge.

Symbol: [Charge-e]

Value: 1.60217662E-19 C

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

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

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How to Evaluate Repeller Voltage?

Repeller Voltage evaluator uses Repeller Voltage = sqrt((8*Angular Frequency^2*Drift Space Length^2*Small Beam Voltage)/((2*pi*Number of Oscillation)-(pi/2))^2*([Mass-e]/[Charge-e]))-Small Beam Voltage to evaluate the Repeller Voltage, The Repeller Voltage formula is defined as the voltage applied to an electrode to push generated ions from the ion chamber toward the analyzer of a mass spectrometer. Repeller Voltage is denoted by V_r symbol.

How to evaluate Repeller Voltage using this online evaluator? To use this online evaluator for Repeller Voltage, enter Angular Frequency (ω), Drift Space Length (L_ds), Small Beam Voltage (V_o) & Number of Oscillation (M) and hit the calculate button.

FAQs on Repeller Voltage

What is the formula to find Repeller Voltage?

The formula of Repeller Voltage is expressed as Repeller Voltage = sqrt((8*Angular Frequency^2*Drift Space Length^2*Small Beam Voltage)/((2*pi*Number of Oscillation)-(pi/2))^2*([Mass-e]/[Charge-e]))-Small Beam Voltage. Here is an example- 58444.61 = sqrt((8*790000000^2*71.7^2*13)/((2*pi*4)-(pi/2))^2*([Mass-e]/[Charge-e]))-13.

How to calculate Repeller Voltage?

With Angular Frequency (ω), Drift Space Length (L_ds), Small Beam Voltage (V_o) & Number of Oscillation (M) we can find Repeller Voltage using the formula - Repeller Voltage = sqrt((8*Angular Frequency^2*Drift Space Length^2*Small Beam Voltage)/((2*pi*Number of Oscillation)-(pi/2))^2*([Mass-e]/[Charge-e]))-Small Beam Voltage. This formula also uses Mass of electron, Charge of electron, Archimedes' constant and Square Root (sqrt) function(s).

Can the Repeller Voltage be negative?

No, the Repeller Voltage, measured in Electric Potential cannot be negative.

Which unit is used to measure Repeller Voltage?

Repeller Voltage is usually measured using the Volt[V] for Electric Potential. Millivolt[V], Microvolt[V], Nanovolt[V] are the few other units in which Repeller Voltage can be measured.

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Repeller Voltage Formula

Repeller Voltage Example

Repeller Voltage Solution

Repeller Voltage Formula Elements

Other formulas in Beam Tube category

How to Evaluate Repeller Voltage?

FAQs on Repeller Voltage

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