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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 centre of the Earth. This gives the total net surface charge carried by the Earth to be [Givenε₀=8.85×10⁻¹² C²/N-m², R_E=6.37×10⁶ m]

Asked in JEE Main Online 2014 · Gauss's law and enclosed charge

Figure: Gauss's law and enclosed charge
Answer: (3) -680 kC

Step-by-step solution

Apply Gauss's law to a sphere just outside the Earth's surface: Q=ε₀ Φ=ε₀ E (4π R_E²), with the sign of Φ set by the field direction.

4π R_E²=4π(6.37×10⁶)²=5.10×10¹⁴ m².

Φ=150×5.10×10¹⁴=7.65×10¹⁶, and Q=8.85×10⁻¹²×7.65×10¹⁶=6.77×10⁵ C.

The field points inward, so the enclosed charge is negative: Q≈-680 kC.

Why the other options are wrong

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