Physics 5C - Lecture 1: Electric Charge and Coulomb’s Law

Electric Force and Charge

One of the fundamental forces in our universe is the electromagnetic (EM) force, which acts between any particles with an electric charge.

We divide the effects of the EM force into electric and magnetic phenomena. We begin by studying the electric force before learning how it is connected to magnetism.

Properties of Electric Charge

  • Electric charge is a fundamental property of particles, just like mass.
  • There are two types of electric charge: positive and negative.
  • The electric force between two charges depends on their signs:
    • Opposite charges attract.
    • Like charges repel.

Quantization and Conservation of Charge

  • Electric charge is quantized: the charge of any particle is always an integer multiple of the fundamental charge: \(e \approx 1.6 \times 10^{-19} C\)
    • Proton charge: $+e$
    • Electron charge: $-e$
  • Conservation of charge: The total electric charge in the universe remains constant.

Coulomb’s Law

We calculate the magnitude of the electric force between two stationary charges using Coulomb’s law:

For two charges $q_1$ and $q_2$ separated by a distance $r$, the force magnitude is: \(F_E = k \frac{|q_1 q_2|}{r^2}\) where:

  • $k$ is the Coulomb constant: \(k \approx 9.0 \times 10^9 \frac{N \cdot m^2}{C^2}\)

Alternative Form Using Permittivity

Sometimes, we use the vacuum permittivity $\epsilon_0$ instead of $k$: \(\epsilon_0 = \frac{1}{4\pi k} \approx 8.85 \times 10^{-12} \frac{C^2}{N \cdot m^2}\)

Rewriting Coulomb’s law: \(F_E = \frac{1}{4\pi\epsilon_0} \frac{|q_1 q_2|}{r^2}\)

Direction of the Electric Force

  • The electric force is attractive for opposite charges and repulsive for like charges.
  • The force vector components can be determined using standard vector decomposition techniques.

Superposition Principle

If multiple charges exert forces on a single charge, the net electric force is the vector sum of the individual forces: \(\vec{F}_{\text{net},1} = \vec{F}_{2 \text{ on } 1} + \vec{F}_{3 \text{ on } 1} + \dots\)

In terms of components: \(F_{1,x} = F_{2,1,x} + F_{3,1,x} + \dots\) \(F_{1,y} = F_{2,1,y} + F_{3,1,y} + \dots\)

This principle applies to any number of charges.

Example Problem

Given: A charge $q_1 = -1.0$ nC is at the origin, and a charge $q_2 = 4.0$ nC is located at $(x, y) = (2.0 \text{ cm}, -3.0 \text{ cm})$.

Find: The components of the electric force on $q_2$.

Conceptual Questions

  1. Two equal charges are placed on the x-axis. Is there any point where a third charge can experience zero force?
  2. What if the two charges have equal magnitude but opposite sign?
  3. What happens if the two charges have different magnitudes but the same sign?

These fundamental ideas set the stage for exploring electric fields and potential in future lectures.