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1. Electric Charges and Fields
medium
If the electric field intensity in a fair weather atmosphere is $100 \,V / m$, then the total charge on the earth's surface is ............ $C$ (radius of the earth is $6400\,km$ )
A
$4.55 \times 10^7$
B
$4.55 \times 10^8$
C
$4.55 \times 10^5$
D
$4.55 \times 10^6$
Solution
(c)
$E=100 \frac{ V }{ m } \quad R=6400 \,km$
By Gauss law
$E A=\frac{q}{\varepsilon_0} \Rightarrow q=E A \varepsilon_0$
$\Rightarrow q=200\left(4 \pi\left(6400 \times 10^3\right)^2\right) \times 8.85 \times 10^{-12}$
$\Rightarrow q=4.55 \times 10^5 \,C$
Standard 12
Physics
