A spherical metal electrostatic probe is charged to a potential of −16 kV-16\text{ kV}−16 kV. The probe is supported by a vertical cylindrical PTFE (Teflon) support column inside a vacuum chamber. The radius of the probe is 0.15 m0.15\text{ m}0.15 m.
Show that the magnitude of the total charge QQQ on the probe is approximately 2.7×10−7 C2.7 \times 10^{-7}\text{ C}2.7×10−7 C.
The probe discharges slowly through the PTFE support column to the grounded chamber floor. It takes exactly 757575 hours for the probe to completely discharge.
Show that the mean current III in the support column is approximately 1.0×10−12 A1.0 \times 10^{-12}\text{ A}1.0×10−12 A.
The average potential difference across the PTFE column during the discharge is 8000 V8000\text{ V}8000 V. The column has a cross-sectional area of 1.5×10−4 m21.5 \times 10^{-4}\text{ m}^21.5×10−4 m2 and a length of 0.50 m0.50\text{ m}0.50 m.
Calculate the resistivity ρ\rhoρ of the PTFE material.