Equation to relate voltage to distance of a spark

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SUMMARY

The discussion centers on calculating the minimum distance for a spark to jump based on voltage in a vacuum. The key equation referenced is derived from the concept of dielectric strength, which quantifies the maximum electric field a material can withstand without breaking down. For air, the dielectric strength is approximately 3 million volts per meter (3 MV/m). Therefore, the minimum distance (d) for a spark to jump can be calculated using the formula d = V / (3 MV/m), where V is the voltage applied.

PREREQUISITES
  • Understanding of dielectric strength and its implications in electrical engineering.
  • Basic knowledge of electric fields and voltage concepts.
  • Familiarity with the properties of materials in a vacuum.
  • Ability to perform unit conversions and basic algebraic calculations.
NEXT STEPS
  • Research the dielectric strength of various gases and materials beyond air.
  • Explore the effects of temperature and pressure on dielectric strength.
  • Learn about the breakdown voltage in different mediums using simulation tools.
  • Investigate practical applications of spark distance calculations in electrical engineering.
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Electrical engineers, physicists, and hobbyists working on projects involving high-voltage applications and spark generation in vacuum environments.

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I need to calculate the minimum distance for which a charge of some voltage will jump. Is there any equation that relates distance of a spark jump to voltage (a fairly generalised equation will do, I don't need to worry about strange shapes of the charged bodies that the charge leaps between or anything). Assume that this occurs in a vacuum. (This isn't homework, just part of a side project, and I am stuck because I can't figure out the above sub-problem, which hopefully isn't too difficult).
 
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