Question

If the electric field intensity in fair weather atmosphere is 100 V/m then the total charge on the earths surface is

Answer 1

Hello Dear,

Your answer is here.

⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔

Given Conditions are


Electric Field Intensity = 100 V/m .

  By Using the Formula , 

   
Electric Field Intensity = k × Q$\frac{k * Q}{r ^{2} }$ 
  
         Where, k = 8.99 × 10⁹ Nm²/C.
 
                       = 9 × 10⁹ Nm²/C ( Approx )

                    r =  radius of the earth 
                     = 6400 km 

                   r = 6.4 × 10⁶ m

            Q = Charge on the earth Surface


Thus , put all the values in the formula →

        100 = ( 9 × 10⁹ × Q ) ÷ ( 6.4 × 10⁶ )²

       ⇒ Q = 455.11 × 10³ C .

  Thus the charge on earth surface is to be 455.11 ×10³ C.


⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔

I hope it helps.

°~Have a Nice Day ~°

Answer 2

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