Paschen's Law and E-field between spheres

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SUMMARY

This discussion focuses on Paschen's Law and the electric field characteristics between two identical spherical electrodes. It is established that when the gap distance between the spheres is significantly smaller than their radii, the electric field can be approximated as uniform due to the concentration of charge on the facing surfaces. This scenario resembles a plane parallel capacitor, where the electric field is uniform in the region of interest. The nuances of electric field behavior in this context are critical for understanding breakdown voltage measurements.

PREREQUISITES
  • Understanding of Paschen's Law and breakdown voltage
  • Familiarity with electric fields and their properties
  • Knowledge of spherical electrodes and their configurations
  • Basic principles of capacitors, particularly plane parallel capacitors
NEXT STEPS
  • Research the mathematical derivation of Paschen's Law
  • Study the behavior of electric fields in non-uniform geometries
  • Explore experimental methods for measuring breakdown voltage between electrodes
  • Investigate the implications of charge distribution on electric field uniformity
USEFUL FOR

Electrical engineers, physicists, and students studying electrostatics, particularly those interested in breakdown phenomena and electric field analysis between spherical electrodes.

Mr Boom
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I am reading up on Paschen's Law and came across some papers measuring breakdown voltage between two identical spherical electrodes. I've read in a couple places that the electric field is uniform when the gap distance is no larger than the radii. Why is that? It seem to me that the field strength would never be uniform.
 
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You are right, it is not exactly uniform. However, when the distance between the surfaces of the spheres is much smaller than the distance of their centres, the positive and negative charge are concentrated close to each other on the facing surfaces. Now if we take only this part of space, smaller than the radius of the sphere, the surfaces are almost parallel and the situation is similar to plane parallel condenser, in which the electric field would be uniform.
 

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