Question

Ratio of the electrostatic to gravitational force between twe electrons placed in air will be, $(m_e=9.1\times {10}^{-31}kg,e=1.6\times {10}^{-19}CandG=6.6\times {10}^{-11}N{m}^2/k{g}^2)$

• A. $4.2\times {10}^{42}$
• B. $4.2\times {10}^{-42}$
• C. $2.4\times {10}^{24}$
• D. $2.4\times {10}^{-24}$

Answer 1

The correct option is A $4.2\times {10}^{42}$

Let the separation between the electrons be $r$.

Electrostatic force between the electrons $F_e=\frac{k{e}^2}{r^2}$

$\therefore$ $F_e=\frac{(9\times {10}^9)\times (1.6\times {10}^{-19}{)}^2}{r^2}$

Also gravitational force $F_g=\frac{G{m}_e^2}{r^2}$

$\therefore$ $F_g=\frac{(6.6\times {10}^{-11})\times (9.1\times {10}^{-31}{)}^2}{r^2}$

Thus ratio $\frac{F_e}{F_g}=\frac{(9\times {10}^9)\times (1.6\times {10}^{-19}{)}^2}{(6.6\times {10}^{-11})\times (9.1\times {10}^{-31}{)}^2}=4.2\times {10}^{42}$