About 5.0 × 10⁴ m above Earth's surface, the atmosphere is sufficiently ionized that it behaves as a conductor. Earth and the ionosphere form a giant spherical capacitor, with the lower atmosphere acting as a leaky dielectric.

(a) Find the capacitance C of the Earthionosphere system by treating it as a parallel plate capacitor. Why is it OK to do that? 

(b) The fair-weather electric field is about 150 V/m, downward. How much energy is stored in this capacitor? 

(c) Due to radioactivity and cosmic rays, some air molecules are ionized even in fair weather. The resistivity of air is roughly 3.0 × 10¹⁴ Ω·m. Find the resistance of the lower atmosphere and the total current that flows between Earth's surface and the ionosphere.

(d) If there were no lightning, the capacitor would discharge. In this model, how much time would elapse before Earth's charge were reduced to 1% of its normal value?