Question

If the electric field intensity in a fair weather atmosphere is $100 \,V / m$, then the total charge on the earth's surface is (radius of the earth is $6400 \,km$ )

• A. $4.55 \times 10^{7} C$
• B. $4.55 \times 10^{8} C$
• C. $4.55 \times 10^{5} C$
• D. $4.55 \times 10^{6} C$

Answer 1

Answer: (C)

$E=100 \frac{ V }{ m } $
$R=6400\, km$
By Gauss law
$E A=\frac{q}{\varepsilon_{0}}$
$ \Rightarrow q=E A \varepsilon_{0}$
$\Rightarrow q=200\left(4 \pi\left(6400 \times 10^{3}\right)^{2}\right) \times 8.85 \times 10^{-12}$
$\Rightarrow q=4.55 \times 10^{5} C$