Question

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

Answer 1

Hello Dear.

Here is your answer---


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Given---

 Electrical field Intensity = 100 V/m.

Using the Formula,
     
       Electrical field Intensity = (k × Q) ÷ r²

Where, k = 8.99 × 10⁹ Nm²/C
                = 9 × 10⁹ Nm²/C   [Approx]
         
       r = radius of the Earth
              = 6400 km.
              = 6.4 × 10⁶ m.
         
     Q = Charge on the earth Surface.

Thus, putting the given value in the given Formula,

       100 = (9 x 10⁹ × Q) ÷ (6.4 × 10⁶)²
      ⇒  Q = 455.11 × 10³ C.

Thus, total charge on the earth surface will be 455.11× 10³ C.


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Hope it helps.


Have a Marvelous day.


Thanks. 

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