Model a thundercloud and the ground below it as a parallel-plate capacitor: the flat…
PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Conductors, capacitance and boundary-value electrostatics · Conductors, capacitance and boundary-value electrostatics
Electricity, Magnetism and Electromagnetism, Ch Conductors, screening and capacitance
Problem
Model a thundercloud and the ground below it as a parallel-plate capacitor: the flat cloud base has area A=12km2 and sits d=1.8km above flat ground, carrying uniform surface charge densities −σ on the cloud base and +σ on the ground. Treat the air as empty space and ignore edge effects, so the field between them is uniform. The measured field strength between cloud and ground is E=2.5×104Vm−1.
((a)) Use Gauss's law for two oppositely charged planes to find σ.
((b)) Find the capacitance of this cloud-ground pair.
((c)) Find the magnitude of the charge on the cloud base and the potential difference between cloud and ground.
((d)) Find the stored energy, and check it by multiplying the field energy density by the volume between cloud and ground.