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Question

# If atmospheric electric field is approximately 150 V/m and radius of the earth is 6400 km, then total charge on the earth's surface is

A
6.8×105 C
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B
6.8×106 C
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C
6.8×104 C
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D
6.8×109 C
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Solution

## The correct option is A 6.8×105 Clet us construct a gaussian sphere passing through surface of earth such that total charge of earth gets enclosed within it. Given, The electric field at earth's surface is, E=150 V/m Radius of the earth, R=6400 km=6400×103 m Applying gauss's law, ϕ=→E.d→A =qinεo ⇒EA=qinεo ⇒E×(4πR2)=qinεo Substituting the values, 150×4×π×(6400×103)2=qinεo ⇒qin=150×4×π×(6400×103)2×8.85×10−12 ∴qin≈6.8×105 C Hence, total charge on the earth's surface is 6.8×105 C.

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