Question

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

• A. $6.8 \times 10^{5}$ coulomb
• B. $6.8 \times 10^{6}$ coulomb
• C. $6.8 \times 10^{4}$ coulomb
• D. $6.8 \times 10^{9}$ coulomb

Answer 1

Answer: (A)

$E=150\, V / m $
$R=6400\,, km4$
Using Gauss' Law
$\Rightarrow E A=\frac{q}{\varepsilon_{0}}$
$\Rightarrow 150\left(4 \pi\left(6400 \times 10^{3}\right)^{2}\right)=\frac{q}{\varepsilon_{0}}$
$q=150 \times 4 \pi \times\left(6400 \times 10^{3}\right)^{2} \times 8.854 \times 10^{-12}$
$q=6.8 \times 10^{5} \,C$