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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 C
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=6400×103 m

Applying gauss's law,

ϕ=E.dA =qinεo

EA=qinεo

E×(4πR2)=qinεo

Substituting the values,

150×4×π×(6400×103)2=qinεo

qin=150×4×π×(6400×103)2×8.85×1012

qin6.8×105 C

Hence, total charge on the earth's surface is 6.8×105 C.

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