Question

two electrons are an angstrom (1x10^-10m) apart. What electrostatic force do they exert on one another?

Answer 1

Answer:

2.30 × 10⁻⁸ N if the two electrons are in a vacuum.

Explanation:

The Coulomb's Law gives the size of the electrostatic force $F$ between two charged objects:

$\displaystyle F = -\frac{k\cdot q_1 \cdot q_2}{r^{2}}$,

where

• $k$ is coulomb's constant. $k = 8.99\times 10^{8}\;\text{N}\cdot\text{m}^{2}\cdot\text{C}^{-2}$ in vacuum.
• $q_1$ and $q_2$ are the signed charge of the objects.
• $r$ is the distance between the two objects.

For the two electrons:

• $q_1 = q_2 = 1.60\times 10^{-19}\;\text{C}$.
• $r = 1\times 10^{-10}\;\text{m}$.

• $\displaystyle F = -\frac{k\cdot q_1 \cdot q_2}{r^{2}} = -\frac{8.99\times 10^{8}\times (1.60\times 10^{-19})^{2}}{(1\times 10^{-10})^{2}} = 2.30\times 10^{-8}\;\text{N}$.

The sign of $F$ is negative. In other words, the two electrons repel each other since the signs of their charges are the same.