Electric Charge and Coulomb’s Law (Sections 16-1 through 16-6)

Electric Charge and Coulomb’s Law

Introduction to Electric Charge

Electricity, derived from the Greek word for 'amber,' refers to phenomena associated with electric charge. The study of electric charge began with observations of static electricity and was formalized through the work of scientists such as Benjamin Franklin.

• Two Types of Charge: There are two kinds of electric charge: positive and negative.

• Conservation of Charge: Electric charge is always conserved in isolated systems.

• Quantization of Charge: Charge exists in discrete packets, with the elementary charge denoted as e.

Example: Rubbing a glass rod with silk transfers electrons, leaving the rod positively charged and the silk negatively charged.

Properties of Electric Charge

• Like charges repel each other; unlike charges attract.

• Large objects are normally electrically neutral, containing equal numbers of positive and negative charges.

• Charge can be transferred by contact or induction.

Conductors and Insulators

Materials can be classified based on their ability to allow electric charge to move:

• Conductors: Materials (such as metals) in which electric charges move freely.

• Insulators: Materials (such as glass or rubber) in which electric charges do not move freely.

Example: When a charged rod is brought near a metal sphere, charges in the sphere redistribute due to induction.

Coulomb’s Law

Coulomb’s Law quantifies the force between two point charges. The force is proportional to the product of the charges and inversely proportional to the square of the distance between them.

Equation:

$F = k_e \frac{|q_1 q_2|}{r^2}$

• F: Magnitude of the electric force between two charges

• q1 and q2: The two point charges

• r: Distance between the charges

• ke: Coulomb’s constant, $k_e \approx 8.99 \times 10^9 \ \mathrm{N \cdot m^2 / C^2}$

Unit of Charge: Coulomb

• The SI unit of electric charge is the coulomb (C).

• The elementary charge (charge of a proton or electron) is $e = 1.602 \times 10^{-19} \ \mathrm{C}$.

Example: The force between two electrons separated by 1 meter is extremely small due to the small value of the elementary charge.

Summary Table: Properties of Electric Charge

Property	Description
Types	Positive and Negative
Conservation	Total charge is conserved in isolated systems
Quantization	Charge exists in integer multiples of $e$
Unit	Coulomb (C)

Additional info: The historical development of electric charge concepts is attributed to early experiments with static electricity and the work of Benjamin Franklin, who introduced the terms 'positive' and 'negative' charge.