Scenario: Two charged particles, a proton and an electron, are separated by a distance of 1 nanometer (1 x 10⁻⁹ m). Calculate the electrostatic force between them.
Given:
* Charge of a proton (q₁): +1.602 x 10⁻¹⁹ C
* Charge of an electron (q₂): -1.602 x 10⁻¹⁹ C
* Distance between the particles (r): 1 x 10⁻⁹ m
* Coulomb's constant (k): 8.98755 x 10⁹ N·m²/C²
Formula:
F = k * |q₁ * q₂| / r²
Calculation:
F = (8.98755 x 10⁹ N·m²/C²) * |(1.602 x 10⁻¹⁹ C) * (-1.602 x 10⁻¹⁹ C)| / (1 x 10⁻⁹ m)²
F ≈ 2.307 x 10⁻⁸ N
Result: The electrostatic force between the proton and the electron is approximately 2.307 x 10⁻⁸ N. Since the charges are opposite, the force is attractive.
Note: This is a simple example to illustrate the application of Coulomb's law. The actual interaction between protons and electrons in a real atom is more complex and involves quantum mechanics.
