Question

Assume that the interstellar space the distance between two electrons is about 0.82 cm. The electric force between the two electrons is... a) repulsive or b) attractive

Answer 1

Assume that in the interstellar space the distance between two electrons is $0.82\mathrm{cm}$. The electric force between these two electrons is: a) repulsive; b) attractive.

Solution: It is known, that charges of the same sign repel each other. Every electron has a negative charge; we can make a conclusion that they are repelled from each other. The repulsive force $F$ can be calculated from the Coulomb's law equation: $F = k_{e} \cdot \frac{q_{1} \cdot q_{2}}{r^{2}} = k_{e} \cdot \frac{e \cdot e}{r^{2}} = k_{e} \frac{e^{2}}{r^{2}}$, where $k_{e} = 9 \cdot 10^{9} \, \text{N} \cdot \text{m}^{2} \cdot \text{C}^{-2}$; $e = 1.6 \cdot 10^{-19} \, \text{C}$ (electric charge of the electron); $r$ is the distance between charges, m.

Then, $F = 9 \cdot 10^{9} \cdot \frac{(1.6 \cdot 10^{-19})^{2}}{(8.2 \cdot 10^{-3})^{2}} = 3.43 \cdot 10^{-24} \, \text{N}$.

Answer: a) Between these two electrons is a repulsive force of $3.43 \cdot 10^{-24} \, \text{N}$.