Physics 212 Fall 2025: Electric Charge and Electric Field Study Notes

Electric Charge and Electric Field

Introduction to Electric Charge

Electric charge is a fundamental property of matter that gives rise to electric forces and electromagnetic phenomena. Understanding electric charge is essential for studying the behavior of atoms, materials, and the interactions that govern much of physics and engineering.

• Definition: Electric charge is a physical property of matter that causes it to experience a force when placed in an electromagnetic field.

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

• Behavior: Like charges repel each other, while opposite charges attract.

• Unit: The SI unit of charge is the Coulomb (C).

• Quantization: Charge is quantized; the smallest unit of charge is the elementary charge $e = 1.6 \times 10^{-19}$ C.

Origin of Electric Charge

Electric charge arises from the subatomic particles within atoms. The structure of the atom explains how materials can become charged.

• Protons: Positively charged particles found in the nucleus ($m_p = 1.67 \times 10^{-27}$ kg).

• Electrons: Negatively charged particles orbiting the nucleus ($m_e = 9.11 \times 10^{-31}$ kg).

• Neutrons: Neutral particles in the nucleus ($m_n = 1.67 \times 10^{-27}$ kg).

• Neutral Atom: In a neutral atom, the number of protons equals the number of electrons.

• Charging: Atoms can lose or gain electrons, resulting in a net positive or negative charge.

• Example: Rubbing a plastic rod with fur transfers electrons, making the rod negatively charged and the fur positively charged.

Methods of Charging

Materials can be charged by several methods, each involving the transfer or redistribution of electrons.

• Friction: Rubbing two materials together can transfer electrons from one to the other.

• Conduction: Direct contact allows electrons to move from a charged object to a neutral one.

• Induction: Bringing a charged object near a neutral one can redistribute charges without direct contact.

• Example: Charging an electroscope by touching it with a charged rod (conduction) or by bringing a charged rod near it (induction).

Conservation and Quantization of Charge

Electric charge obeys two important principles: conservation and quantization.

• Conservation of Charge: The net electric charge of an isolated system remains constant.

• Equation: $Q = q_1 + q_2 + q_3 + \ldots + q_n = \text{const}$

• Quantization of Charge: Any charge $Q$ can be written as a multiple of the elementary charge $e$.

• Equation: $Q = n e$, where $n$ is an integer.

Electrical Properties of Materials

Materials are classified based on their ability to conduct electric charge.

• Conductors: Materials with free electrons that can move easily (e.g., metals).

• Insulators: Materials with very few free electrons; charge does not move easily (e.g., glass, rubber).

• Semi-conductors: Materials with intermediate properties, often dependent on impurities and temperature.

Coulomb's Law

Coulomb's Law describes the force between two point charges. It is a fundamental law in electrostatics.

• Statement: The magnitude of the electrostatic force $F$ between two point charges $q_1$ and $q_2$ separated by a distance $r$ is given by:

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

• Constant: $k = 8.99 \times 10^9$ N·m2/C2 (in SI units)

• Direction: The force acts along the line joining the two charges.

• Permittivity: $k = \frac{1}{4 \pi \varepsilon_0}$, where $\varepsilon_0 = 8.85 \times 10^{-12}$ C2/N·m2 is the permittivity of free space.

• Example Calculation: The force between two 1 C charges separated by 0.1 m is:

$F = k \frac{(1\,\text{C})(1\,\text{C})}{(0.1\,\text{m})^2} = 8.99 \times 10^9 \frac{1}{0.01} = 8.99 \times 10^{11}$ N$

Fundamental Forces of Nature

All interactions in the universe are governed by four fundamental forces.

Force	Relative Strength	Range	Particles Affected	Role
Strong Nuclear	Strongest	$\sim 10^{-15}$ m	Protons, Neutrons	Binds nucleus together
Electromagnetic	Second strongest	Infinite	Charged particles	Responsible for electric and magnetic phenomena
Weak Nuclear	Weaker	$\sim 10^{-18}$ m	All fermions	Responsible for radioactive decay
Gravitational	Weakest	Infinite	All mass	Responsible for attraction between masses

Orders of Magnitude

Orders of magnitude are used to compare the scale of physical quantities such as mass and length.

Object	Mass (kg)	Length (m)
Hydrogen atom	$\sim 10^{-27}$	$\sim 10^{-10}$
Grain of sand	$\sim 10^{-6}$	$\sim 10^{-3}$
Human	$\sim 10^{2}$	$\sim 1$
Earth	$\sim 10^{24}$	$\sim 10^{7}$
Milky Way Galaxy	$\sim 10^{42}$	$\sim 10^{21}$

Example PRS Questions

• Forces can be added together only if they are: acting on the same object.

• A plastic strip was rubbed with cotton and became positively charged. Why? The plastic strip lost electrons to the cotton during the charging process.

Summary of Key Points

• Electric charge comes in two types: positive and negative.

• Like charges repel; opposite charges attract.

• Charge is conserved and quantized.

• Materials can be charged by friction, conduction, or induction.

• Coulomb's Law quantifies the force between two point charges.

• Four fundamental forces govern all interactions in nature.

Additional info: Some context and examples have been expanded for clarity and completeness.