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, R_E = 6.37 × 10⁶m]

Options

• +670 kC

• -670 kC

• -680 kC

• +680 kC

Answer 1

-680 kC

Explanation:

Given,

Electric field E = 150 N/C

Total surface charge carried by earth q = ?

By Gauss law

`"q"_"in"/epsilon_0= intvec"E".vec"da" => "q"_"in"/epsilon_0`

= |E| × 4πr²  

= q_in = 4πε₀ |E| r² 

= 4π × 8.85 × 10^-12 × 150 × (6.37 × 10⁶)² ≃ 680 Kc.

As electric field directed inward hence

q = -680 Kc