Physics 1409: Electricity, Magnetism, and Electric Fields – Study Notes

Course Overview

General Physics for Natural and Behavioral Sciences II

This course covers fundamental concepts in electricity, magnetism, optics, and modern physics, providing a foundation for students in natural and behavioral sciences.

• Instructor: Dr. John Vasut

• Topics: Electrostatics, Electrical Currents and Circuits, Magnetism and Induction, Electromagnetic Waves, Optics, Modern Physics (Relativity, Radioactivity)

Course Policies and Structure

Homework and Labs

Active engagement with homework and laboratory exercises is essential for mastering physics concepts.

• Homework: Use the MasteringPhysics online system. Collaboration is encouraged, but individual completion is required.

• Labs: Must pass with at least 60% and attend at least 75% of lab sessions.

Tests and Re-tests

• Tests: Include multiple-choice and worked problems. Partial credit may be given for showing work.

• Re-tests: 10-point penalty if retaking without a valid excuse after the original test.

Review of Prerequisite Concepts

Significant Figures and Units

Accurate calculations in physics require proper use of significant figures and units.

• Significant Figures: Reflect measurement uncertainty. Carry one extra digit for intermediate calculations.

• Examples: $1.0/3.0 = 0.33$ (not $0.3333333$), $25.7 - 1.181 = 24.5$, $ext{sin}~45.0^ ext{o} = 0.7$

• Units: Always include correct units (e.g., m, N, C). Example: $170~ ext{cm}$, $170~ ext{m}$, $170~ ext{C}$

Example Application: The "Gimli Glider" incident (Air Canada 143) highlights the importance of correct units in real-world scenarios.

Vectors in Physics

Vector Quantities and Operations

Vectors are essential for describing physical quantities such as force, velocity, and electric field.

• Vector Addition: $\vec{R} = \vec{R}_x + \vec{R}_y$

• Angle Calculation: $\theta = \tan^{-1}(R_y/R_x)$

• Equations of Motion: $F = ma$, $T = F \cdot L \sin \theta$, $s = v_0 t + \frac{1}{2} a t^2$

Electric Forces and Fields

Electric Charge and Conservation

Electric charge is a fundamental property of matter, conserved in all physical processes.

• Types of Charge: Two types: glass-like (vitreous, positive) and amber-like (resinous, negative)

• Law of Conservation of Charge: The net charge produced in any process is always zero.

• Charge Quantization: Charge exists in discrete units: $e = 1.602 \times 10^{-19}~\text{C}$ (electron), $q_e = -e$, $q_p = +e$ (proton)

Conductors, Insulators, and Semiconductors

Materials are classified by their ability to conduct electric charge.

Type	Examples	Resistivity (Ω·m)
Conductors	Silver, Copper, Gold, Aluminum, Iron, Lead	~$10^{-8}$
Insulators	Plastics, Glass, Teflon, Rubber	~$10^{10}$ to $10^{13}$
Semi-conductors	Carbon, Germanium, Silicon	~$10^{-1}$ to $10^3$

Coulomb's Law

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

• Formula: $F = k \frac{|q_1 q_2|}{r^2}$, where $k = 8.99 \times 10^9~\text{N·m}^2/\text{C}^2$

• Direction: Like charges repel, opposite charges attract.

• Example: Force between two $1~\text{C}$ charges $1~\text{m}$ apart: $F = 9 \times 10^9~\text{N}$

Additional info: The force is a vector; sum forces from multiple charges using vector addition and symmetry.

Electric Field

The electric field describes the force per unit charge at a point in space.

• Definition: $\vec{E} = \frac{\vec{F}}{q}$ (units: N/C)

• Point Charge: $E = k \frac{Q}{r^2}$

• Superposition Principle: $\vec{E}_{\text{total}} = \vec{E}_1 + \vec{E}_2 + \vec{E}_3 + ...$

• Direction: For positive $q$, $\vec{F}$ and $\vec{E}$ are in the same direction; for negative $q$, they are opposite.

Field Lines and Visualization

Field lines help visualize the direction and strength of electric fields.

• Direction: Outward from positive charges, inward toward negative charges.

• Density: Closer lines indicate stronger fields.

• Example: Uniform field between parallel plates; field lines are parallel and evenly spaced.

Electric Fields in Conductors

In electrostatic equilibrium, the electric field inside a conductor is zero.

• Surface Charges: Charges reside on the surface.

• Field Direction: The field at the surface is perpendicular to the surface.

• Equilibrium: Internal field cancels external field, resulting in zero net field inside.

Gauss's Law

Electric Flux and Gauss's Law

Gauss's Law provides a powerful method for calculating electric fields, especially with symmetric charge distributions.

• Electric Flux: $\Phi_E = E \cdot A \cdot \cos \theta$

• Gauss's Law: $\oint \vec{E} \cdot d\vec{A} = \frac{q_{\text{in}}}{\varepsilon_0}$, where $\varepsilon_0 = 8.85 \times 10^{-12}~\text{C}^2/(\text{N·m}^2)$

• Application: For a point charge, $\Phi_E = \frac{q}{\varepsilon_0}$

Quantity	Symbol	Units
Electric Field	$E$	N/C
Electric Flux	$\Phi_E$	N·m2/C
Permittivity of Free Space	$\varepsilon_0$	C2/(N·m2)

Conceptual Questions and Applications

Induced Polarization and Forces

Charged objects can induce polarization in nearby neutral objects, leading to attractive forces.

• Example: A charged balloon sticks to hair or picks up paper due to induced polarization.

• Polar Molecules: Molecules with uneven charge distribution can be influenced by external fields.

Problem Solving Strategies

• Draw diagrams to visualize charge configurations and field directions.

• Use symmetry to simplify calculations.

• Apply vector addition for forces and fields from multiple sources.

Summary Table: Key Equations

Concept	Equation (LaTeX)
Coulomb's Law	$F = k \frac{|q_1 q_2|}{r^2}$
Electric Field (point charge)	$E = k \frac{Q}{r^2}$
Force from Electric Field	$F = qE$
Electric Flux	$\Phi_E = E \cdot A \cdot \cos \theta$
Gauss's Law	$\oint \vec{E} \cdot d\vec{A} = \frac{q_{\text{in}}}{\varepsilon_0}$

Additional Info

• Cartoon included in the materials humorously illustrates static electricity and the concept of resistors, which is relevant to the study of electric charge and resistance.