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- Trying to calculate the charge density upon the leaves as a function of voltage applied to a DIY metal leaf or pith ball electroscope without knowing the voltage applied (relative to earth ground) beforehand.
I'm trying to build a DIY metal leaf or pith ball electroscope. I want to provide it with a circular arc voltage scale visible directly behind the (deflected) ends of the leaves. To calibrate the scale with ballpark accuracy, I want to determine the charge density upon the leaf pair (or pith balls), measure their weight, thickness and area (or volume) and apply the equations of deflection (of the pith balls):
https://www.physicsforums.com/threads/force-components-of-hanging-pith-balls.779971/
Or a hairier integral as to two leaves deflecting at varying angles. Ultimately, I want to determine the voltage applied to it (relative to Earth ground) provided by a cheap, high-voltage, step-up, transformer-terminated (and earth-grounded output terminal), electrostatic generator module (or Van der Graff generator) without buying an expensive electroscope and measuring the voltage that way to calibrate the circular arc scale. I'm aware of the equation: C = Q / V = e A / d = e0 er h w / d, where e0, er, h, w and d are permeability of free space, relative permeability, plate height, width and distance between plates. But in this case, one plate is the two leaves (or pith balls) with identical (repulsive) charge and the matching plate is Earth ground an 'infinite' distance away. Capacitance C goes to zero as d goes to infinity, and thus so does charge C, according to the capacitor equation. It's not really a capacitor per se. But the leaves have a charge obviously. Can't seem to find the physics/engineering information that I need to determine the charge and voltage (both being unknowns). The capacitor equation always comes up when I search on 'plates', 'charge', 'voltage', 'electroscope', etc. Any ideas? Or is that too vague?
https://www.physicsforums.com/threads/force-components-of-hanging-pith-balls.779971/
Or a hairier integral as to two leaves deflecting at varying angles. Ultimately, I want to determine the voltage applied to it (relative to Earth ground) provided by a cheap, high-voltage, step-up, transformer-terminated (and earth-grounded output terminal), electrostatic generator module (or Van der Graff generator) without buying an expensive electroscope and measuring the voltage that way to calibrate the circular arc scale. I'm aware of the equation: C = Q / V = e A / d = e0 er h w / d, where e0, er, h, w and d are permeability of free space, relative permeability, plate height, width and distance between plates. But in this case, one plate is the two leaves (or pith balls) with identical (repulsive) charge and the matching plate is Earth ground an 'infinite' distance away. Capacitance C goes to zero as d goes to infinity, and thus so does charge C, according to the capacitor equation. It's not really a capacitor per se. But the leaves have a charge obviously. Can't seem to find the physics/engineering information that I need to determine the charge and voltage (both being unknowns). The capacitor equation always comes up when I search on 'plates', 'charge', 'voltage', 'electroscope', etc. Any ideas? Or is that too vague?