Overview
This lecture introduces Coulomb's Law, which describes the electrostatic force between two point charges, and applies it to solve both one-dimensional and two-dimensional force problems.
Coulomb’s Law: The Electrostatic Force
- Coulomb’s Law gives the formula: F = k * |q₁| * |q₂| / r², where F is the force, k is Coulomb’s constant, q₁ and q₂ are charges, and r is separation distance.
- Coulomb’s constant, k, equals 8.99 × 10⁹ N·m²/C².
- The force can be attractive (opposite charges) or repulsive (like charges).
- Like charges repel; unlike (opposite) charges attract.
- The electrostatic force is proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
- Doubling either charge doubles the force; doubling the distance decreases the force by a factor of four.
- Electrostatic force is similar to gravitational force but can be both attractive and repulsive.
Example Calculations: One-Dimensional Problems
- For two charges of +1.0 C each, separated by 0.10 m, F = 8.99 × 10⁷ N (very large due to the high charge).
- For two charges of +1.0 μC each, separated by 0.10 m, F = 0.899 N.
- Use SI units for all quantities; convert μC (microcoulombs) to C before calculating.
Two-Dimensional Coulomb’s Law Application
- When a charge experiences forces from multiple other charges, calculate the force from each using Coulomb’s law, then combine as vectors.
- Use vector addition (Pythagorean theorem if forces are perpendicular) to find the resultant force.
- Find magnitude using F = √(F₁² + F₂²); find direction using θ = tan⁻¹(F_y / F_x).
Two-Dimensional Mechanics Problem Example
- For two spheres with identical charge hanging from strings, the repulsive electrostatic force and tension components create equilibrium at an angle.
- Draw a free-body diagram; resolve tension into x and y components.
- Use ΣF_x = 0 and ΣF_y = 0 to set up equations.
- Distance between spheres is calculated from geometry (using string length and angle).
- Solve for the charge Q using the equilibrium equations and Coulomb’s law.
Key Terms & Definitions
- Coulomb’s Law — The law stating the electrostatic force between two point charges is proportional to the product of their charges and inversely proportional to the square of their separation.
- Coulomb’s Constant (k) — The proportionality constant in Coulomb’s law; 8.99 × 10⁹ N·m²/C².
- Electrostatic Force — The force between stationary electric charges, can be attractive or repulsive.
- μC (Microcoulomb) — 1 μC = 1 × 10⁻⁶ C.
Action Items / Next Steps
- Practice applying Coulomb’s law to both 1D and 2D problems.
- Review free-body diagrams and vector addition for forces.
- Complete assigned problems involving equilibrium of charged objects.