Question

The ratio of the electric force between two electrons to the gravitational force between them is of the order of

• A. ${10}^{42}$
• B. ${10}^{40}$
• C. ${10}^{36}$
• D. ${10}^{32}$

Answer 1

Answer: (A)

Charge on an electron $q=-1.6\times {10}^{-19}C$

Mass of an electron ,$m=9.1\times {10}^{-31}kg$

gravitational constant, $g=6.67\times {10}^{-11}$

Let the distance between two electrons $=r$

$\therefore$ electric force, $K^{\prime }=9\times {10}^9$

gravitational force, $F_q=\frac{K{\left(q\right)}^2}{r^2}$

$\begin{array}{c}\\ Now,\frac{F_e}{F_g}=\frac{k{q}^2}{r^2}\times \frac{r^2}{G{m}^2}\\ =\frac{9\times {10}^9\times {\left(-1.6\times {10}^{-19}\right)}^2}{6.67\times {10}^{-11}\times {\left(9.1\times {10}^{-31}\right)}^2}\\ =4.17\times {10}^{42}\end{array}$

Hence Option $A$ is correct .