7.3.1 Coulomb's law

Definition

Coulomb's Law states that the force between two point charges in a vacuum is:

• Directly proportional to the product of the two charges.
• Inversely proportional to the square of the distance between them. The mathematical expression for Coulomb's law is:

$$F = \frac{1}{4\pi \varepsilon_0} \frac{Q_1 Q_2}{r^2}$$

Where:

• F is the force between the charges,
• $\varepsilon_0$ is the permittivity of free space,
• $Q_1$and $Q_2$ are the charges,
• $r$ is the distance between the centres of the charges.

Comparing Electrostatic and Gravitational Forces

Consider two protons, 2 pm (or 2 × 10⁻¹² m) apart.

1. Gravitational Force Calculation:

$$F = \frac{G m_1 m_2}{r^2} = \frac{6.67 \times 10^{-11} \times (1.67 \times 10^{-27})^2}{(2 \times 10^{-12})^2} = :highlight[4.65 \times 10^{-41} \, \text{N}]$$

2. Electrostatic Force Calculation:

$$F = \frac{1}{4 \pi \varepsilon_0} \frac{Q_1 Q_2}{r^2} = \frac{1}{4 \pi \times 8.85 \times 10^{-12}} \frac{(1.6 \times 10^{-19})^2}{(2 \times 10^{-12})^2} = :highlight[5.75 \times 10^{-5} \, \text{N}]$$

3. Ratio of Electrostatic Force to Gravitational Force:

$$\frac{F_{\text{electrostatic}}}{F_{\text{gravitational}}} = \frac{5.75 \times 10^{-5}}{4.65 \times 10^{-41}} = :highlight[1.24 \times 10^{36}]$$

Conclusion:

The electrostatic force between two protons is approximately 1.24 × 10³⁶ times stronger than the gravitational force. This significant difference is why electrostatic forces dominate interactions at the atomic and subatomic levels.