Charging or Discharging Particles

In order to achieve breakdown, electrons (either from the air or from the body) must be accelerated to a sufficient velocity to ionize the air and breed more electrons by any one of several processes. In an actual gas, however, some of the kinetic energy of the electrons is lost in collisions with air molecules without resulting in ionization. This combined effect has been expressed in terms of the Townsend ionization coefficient. As a body becomes smaller, its curvature increases and the electric field intensity drops off more rapidly with distance from the surface consequently, to accelerate electrons a given amount, the body surface field intensity must be higher than for a flat surface. Actually, because of increased attenuation resulting from the increased distance that an electron must travel through air to achieve a given acceleration, the required surface intensity must increase even faster. 

No attempts to calculate those limiting surface field intensities or gradients for small particles have been reported in the literature. However, point-to-plane corona has been studied in detail. Loeb (L8) has proposed a method for calculating positive corona threshold limits making use of established values of the Townsend first ionization coefficient. Loeb s threshold formula is 

5 Actually, with flat plates, the first sign of breakdown is a spark and there is no initial 

Negative corona is considerably more complicated and depends more on the emission properties of the discharge surface and of the gas. White (W4) gives a detailed discussion of corona mechanisms. In general, the negative corona threshold is higher than the positive. 

As previously discussed, for two equally sized, equally and oppositely charged conducting spheres, the capacitance is given by 

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