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Question:

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 ε₀=8.85×10⁻¹² C²/N⁻m², Rₑ=6.4×10⁶m]

+680kC

+660kC

+60kC

+80kC

Solution:

From Gauss' Law, the electric field entering the Earth's atmosphere is E. The flux of this field is, ∫E.ds = E × 4πR². This should be equal to the charge enclosed inside the Earth divided by ε. Hence, E × 4πR² = q/ε. Hence, putting back the value of knowns, the value of q = +680 × 10³ C