Question

if atmospheric electric field is approximately 100 volt/m and radius of the earth is 6400km then the total charge on the Earth's surface is?

Answer 1

Electric field intensity , E = 100 V/m
Actually, Earth's surface, the ioniosphere resembles a spherical capacitor.
so, surface charge density on Earth's surface is given by
σ = ∈₀E [ ∵ relation between electric field and surface charge density and permittivity of medium is E = σ/∈₀ ]

∴ σ = 8.85 × 10⁻¹² × 100 C/m²
= 8.85 × 10⁻¹⁰ C/m²

We know,
Radius of earth , R = 6400 km = 6.4 × 10⁶ m
hence, charge on Earth's surface = surface charge density × surface area of earth
= σ × 4πR²
= 8.85 × 10⁻¹⁰ × 4 × 3.14 × (6.4 × 10⁶)² C
= 8.85 × 12.56 × 6.4 × 6.4 × 10² C
= 4.55294 × 10⁵ C