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The magnitude of the average electric field normally present in the atmosphere just above the surface of the Earth is about 150 N / C , directed inward towards the center of the Earth. This gives the total net surface charge carried by the Earth to be : [Given : ∈ O = 8.85 × 1 0 - 1 2 C 2 / N-m 2 , R E = 6.37 × 1 0 6 m ]

Options

  1. A- 680   kC
  2. B+   670   k C
  3. C+   680   kC
  4. D-   670   kC

Correct answer

A. - 680   kC

Step-by-step solution

E = 150 N / C We know that ϕ = E → · A → = E × 4 π r 2 = 1 5 0 × 4 π × R e 2 Now, ϕ = Q in ∈ o Q in = ϕ ∈ o = 1 5 0 × 4 π R e 2 × 8.85 × 1 0 - 1 2 C = 1 5 0 × 4 π 6.37 × 1 0 6 2 × 8.85 × 1 0 - 1 2 = 6 0 0 π × 6.37 × 6.37 × 8.85 C = 6 8 0 kC As Electric field is inward, Q will be negative

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