Question

Two electrons are kept at a separation of 10 fm (1 fm = 10^-15 m). Determine the gravitational force of interaction between these two electrons. (mass of an electron = 9.1×10^-31 kg.)

Answer 1

Step 1: Given data:
Mass of the electron $\left(me\right)=9.1\times {10}^{-3}\mathrm{kg}.$
Distance of separation between two electrons $=1\times {10}^{-15}\mathrm{m}.$

Formula:
Gravitational force of interaction between two masses is.
$\mathrm{F}=\frac{{\mathrm{Gm}}_1{\mathrm{m}}_2}{{\mathrm{r}}^2}$
Were, $\mathrm{G}–\mathrm{Gravitational}\mathrm{constant}.$

Step 2: Calculating force
Two electrons have same mass $(m_1=m_2=m_e)$.
$$\begin{gathered} \mathrm{F}=\frac{{\mathrm{Gm}}_1{\mathrm{m}}_2}{{\mathrm{r}}^2}=\frac{(6.6743\times {10}^{-11})\left(9.1\times {10}^{-31}\right)\left(9.1\times {10}^{-31}\right)}{{\left(1\right)}^2} \\ {\text{F =5.5×10}}^{-43}\text{N} \end{gathered}$$

Hence the gravitational force of interaction between these two electrons is $5.5\times \times {10}^{-43}N$