Section 3.1: Coulomb’s Law
Coulomb’s Law describes the electrostatic force between two point charges. The force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them:
\[ F = k \frac{|q_1 q_2|}{r^2} \]
- \(F\) = magnitude of the force (N)
- \(q_1, q_2\) = charges (C)
- \(r\) = distance between charges (m)
- \(k = 8.99 \times 10^9 \, \text{N·m²/C²}\)
Example: Electrostatic Force
Calculate the force between two charges: \(q_1 = 2 \, \mu\text{C}\) and \(q_2 = 3 \, \mu\text{C}\), separated by 0.5 m.
\[ F = \frac{(8.99 \times 10^9)(2 \times 10^{-6})(3 \times 10^{-6})}{(0.5)^2} = 0.21576 \, \text{N} \approx 0.216 \, \text{N} \]
Practice Problems
- Two charges of +5 μC and -3 μC are placed 0.2 m apart. Calculate the magnitude and direction of the force.
- If the distance between two charges is doubled, how does the force change?
- Three point charges are placed at the vertices of a triangle. Calculate the net force on one charge due to the other two.
- Explain why Coulomb’s law only applies to point charges and spherically symmetric charge distributions.
- A charge of 1 μC is placed at the center of a spherical shell with total charge +4 μC uniformly distributed. Find the force on the central charge.