If atmospheric electric field is approximately 150V/m and radius of the earth is 6400km, then total charge on the earth's surface is
A
6.8×105C
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B
6.8×106C
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C
6.8×104C
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D
6.8×109C
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Solution
The correct option is A6.8×105C let 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=6400×103m
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≈6.8×105C
Hence, total charge on the earth's surface is 6.8×105C.