Paschen's Law Calculator

Paschen's Law Equation:

\[ V_{min} = \frac{e \times B}{A} \] \[ \text{where at } pd_{min} = \frac{e}{A} \]

Secondary Electron Emission Coefficient (e):

unitless

Constant B:

V/(Torr·cm)

Constant A:

1/(Torr·cm)

Minimum Breakdown Voltage (V_min):

Minimum Pressure-Distance Product (pd_min):

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1. What is Paschen's Law?

Paschen's Law describes the breakdown voltage necessary to initiate an electric discharge between two electrodes in a gas as a function of pressure and gap distance. It shows that the breakdown voltage is dependent on the product of the gas pressure and the distance between the electrodes.

2. How Does the Calculator Work?

The calculator uses Paschen's Law equations:

\[ V_{min} = \frac{e \times B}{A} \] \[ pd_{min} = \frac{e}{A} \]

Where:

\( V_{min} \) — Minimum breakdown voltage (V)
\( pd_{min} \) — Minimum pressure-distance product (Torr·cm)
\( e \) — Secondary electron emission coefficient (unitless)
\( B \) — Constant (V/(Torr·cm))
\( A \) — Constant (1/(Torr·cm))

Explanation: The equations determine the minimum voltage required for electrical breakdown in a gas and the corresponding pressure-distance product at which this minimum occurs.

3. Importance of Paschen's Law

Details: Paschen's Law is crucial for designing electrical equipment, vacuum systems, and high-voltage applications. It helps engineers determine safe operating conditions to prevent unwanted electrical discharges.

4. Using the Calculator

Tips: Enter the secondary electron emission coefficient (e), constant B, and constant A for your specific gas and electrode material. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for A and B?
A: For air, typical values are A ≈ 15 (1/(Torr·cm)) and B ≈ 365 (V/(Torr·cm)). These vary for different gases.

Q2: What is the significance of the minimum in Paschen's curve?
A: The minimum represents the most favorable conditions for electrical breakdown, requiring the lowest voltage.

Q3: How does temperature affect Paschen's Law?
A: Temperature affects gas density, which is related to pressure. The law holds when using corrected pressure values.

Q4: Can Paschen's Law be applied to all gases?
A: Yes, but each gas has its own characteristic A and B constants that must be used.

Q5: What happens at very high pressures or small gaps?
A: The law breaks down at extreme conditions where other physical processes dominate.