Question

If $F_g$ and $F_e$ are gravitational and electrostatic forces between two electrons at a distance $0.1$ $m$ then $F_g/F_e$ is in the order of :

• A. ${10}^{43}$
• B. ${10}^{-43}$
• C. ${10}^{35}$
• D. ${10}^{-35}$

Answer 1

The correct option is B ${10}^{-43}$

Gravitational force $F_g=\frac{G{m}^2}{r^2}$

Electrostatic force $F_e=\frac{K{q}^2}{r^2}$

$\frac{F_g}{F_e}=\frac{G{m}^2}{K{q}^2}$

where $G=$Universal gravitational constant and $K=1/4\pi {ϵ}_0$

$G=6.67\times {10}^{-11}$ and $K=9\times {10}^9$

Mass of an electron is $9.1\times {10}^{-31}$ and Charge of an electron is $1.6\times {10}^{-19}$

Hence, $F_g/F_e=G{m}^2/K{q}^2$ is of the order of ${10}^{-11-62-9+38}={10}^{-43}$