Distance Between Anode And Cathode Calculator

Formula Used:

\[ d = \frac{1}{B_{0c}} \times \sqrt{2 \times \frac{m_e}{e} \times V_0} \]

Distance Between Anode and Cathode:

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1. What is the Distance Between Anode and Cathode Calculation?

The distance between anode and cathode calculation determines the optimal spacing between these electrodes in vacuum tube devices like magnetrons. This distance is crucial for proper electron flow and device operation, particularly in microwave generation applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d = \frac{1}{B_{0c}} \times \sqrt{2 \times \frac{m_e}{e} \times V_0} \]

Where:

\( d \) — Distance between anode and cathode (m)
\( B_{0c} \) — Hull cutoff magnetic flux density (T)
\( m_e \) — Mass of electron (9.10938356×10⁻³¹ kg)
\( e \) — Charge of electron (1.60217662×10⁻¹⁹ C)
\( V_0 \) — Anode voltage (V)

Explanation: This formula calculates the critical distance where electrons just fail to reach the anode under the influence of both electric and magnetic fields.

3. Importance of Distance Calculation

Details: Proper anode-cathode spacing is essential for efficient electron flow, optimal microwave generation, and preventing arcing or short circuits in vacuum tube devices.

4. Using the Calculator

Tips: Enter Hull cutoff magnetic flux density in Tesla and anode voltage in Volts. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is Hull cutoff magnetic flux density?
A: It's the minimum magnetic field strength required to prevent electrons from reaching the anode in a crossed-field device.

Q2: Why is electron mass and charge important in this calculation?
A: These fundamental constants determine how electrons respond to electric and magnetic fields, affecting their trajectory between electrodes.

Q3: What applications use this calculation?
A: Primarily used in magnetron design for microwave ovens, radar systems, and other microwave generation equipment.

Q4: How does anode voltage affect the distance?
A: Higher anode voltages require greater distances to maintain the same cutoff conditions, as electrons gain more energy.

Q5: Are there practical limitations to this formula?
A: Yes, real-world factors like electrode geometry, space charge effects, and manufacturing tolerances may require adjustments to the theoretical calculation.