First slide

Electrostatic potential

Question

Let us suppose the earth (radius 6400 km) had a net charge equivalent to one electron n/m² of its surface area. Its potential in volt will be

Moderate

A

0.12
B

-0.12
C

+1.2
D

-1.2

Solution

$V = \frac{1}{4 {πε}_{0}} \times \frac{Q}{R} = \frac{1}{4 {πε}_{0}} \times \frac{4 {πR}^{2} e}{R}$
$\begin{array}{l} = \frac{1}{4 {πε}_{0}} \times 4 πRe \\ = (9 \times 10^{9}) 4 \times \frac{22}{7} \times (6 \cdot 4 \times 10^{6}) (- 1 \cdot 6 \times 10^{- 19}) \\ = - 0 .12 volt. \end{array}$

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