A volcanic ash plume rising above an active crater is modelled as an ideal parallel plate capacitor with circular horizontal layers of charge. In this model, the upper region of the plume is negatively charged and the lower region is positively charged.
The model is based on the following data:
Take the permittivity of free space as ε0=8.85×10−12 F m−1\varepsilon_0 = 8.85 \times 10^{-12}\text{ F m}^{-1}ε0=8.85×10−12 F m−1.
State the direction of the electric field lines between the upper and lower regions of this volcanic plume model.
Suggest why the actual electric field lines in a real volcanic ash plume would differ from those of the ideal parallel plate capacitor model.
Calculate the potential difference (p.d.) VVV between the upper and lower regions.
Calculate the capacitance CCC of this model capacitor.
Calculate the magnitude of the charge QQQ on one of the regions of the model.
Volcanic lightning is an electrical discharge that occurs between the charged ash plume and the volcano's crater rim on the Earth's surface. Another ash plume has a charge of 160 C160\text{ C}160 C and is at an effective height of 2.4 km2.4\text{ km}2.4 km above the rim. The crater rim has an electrical potential of 0 V0\text{ V}0 V. Assuming this plume acts as a point charge, calculate the magnitude of the electrical potential VVV of this plume relative to the crater rim.
A volcanic lightning strike of duration 60 ms60\text{ ms}60 ms occurs. The plume discharges at a constant rate and is completely uncharged after the strike. Calculate the number of electrons reaching the ground in 1.8 ms1.8\text{ ms}1.8 ms.
