-- ELECTRIC FIELDS --

Electric Fields – Lecture

14 Topics

P19-010 – Introduction to Electric Charge

P19-020 – Electric Charge

P19-030 – Electric Fields & Electric Field Lines

P19-040 – Principle of Superposition

P19-050 – Electric Field & Symmetry

P19-060 – Electric Field Created by a Point Charge

P19-070 – Electric Force

P19-080 – Electric Force between Two Point Charges: Coulomb’s Law

P19-140 – Electric Dipole in a Uniform Electric Field

P19-150 – Application: dielectric materials

P19-100 – Computation: finite rod of charge

P19-110 – Computation: semicircle of charge

P19-120 – Computation: ring of charge

P19-130 – Computation: disk of charge

Electric Fields – Problems

8 Topics

P19R2015 – Turning Around in E

P19R2015 – Projectile Motion Through E

P19B2018 – Five Point Charges

P19R2015 – Three Point Charge Distribution

P19R2017 – Square Configuration of Point Charges

P19S2014 – Infinite Sheet & Point Charge

P19S2017 – Charged Ring and Three Point Charges

P19S2017 – Four Infinite Sheets

-- GAUSS'S LAW --

Gauss’s Law – Lecture

10 Topics

P20-010 – Useful Definitions

P20-020 – Electric Flux

P20-030 – How Electric Flux Varies

P20-040 – Classic Computations of Electric Flux

P20-045 – Gauss’s Law

P20-050 – Application: infinite line of charge

P20-060 – Application: infinite rod of charge

P20-070 – Application: infinite sheet of charge

P20-080 – Application: solid sphere of charge

P20-090 – Electric Field at the Surface of a Conductor

Gauss’s Law – Problems

9 Topics

P20R2015 – About Electric Flux

P20S2014 – Two Concentric Insulators

P20R2015 – Infinite Slab of Charge

P20B2015 – Spherical Off-Center Cavity

P20B2020 – Concentric Spheres

P20R2015 – Spherical Metallic Shell

P20S2017 – Charged Sphere & Conducting Shell

P20B2016 – Two Parallel Slabs

P20B2023 – Charge Hanging from a String

-- ELECTRIC POTENTIAL --

Electric Potential – Lecture

14 Topics

P21-010 – Conceptual Introduction to Electric Potential

P21-020 – Electric Potential Created by a Charge Distribution

P21-030 – Deriving Electric Potential Energy

P21-040 – Electric Potential Difference: voltage

P21-050 – Electric Potential & Electric Potential Energy

P21-070 – Principle of Superposition

P21-080 – Equipotentials

P21-090 – Electric Potential Created by a Point Charge

P21-100 – Electric Potential Created by a Dipole

P21-110 – Electric Potential of a Line of Charge

P21-120 – Electric Potential of a Semicircular Wire

P21-130 – Electric Potential of a Ring of Charge

P21-160 – Electronvolt and Conservation of Energy

P21-170 – Electrostatic Energy of a System of Point Charges

Electric Potential – Problems

9 Topics

P21B2016 – Connecting Charged Spheres

P21R2015 – Electrostatics of Three Point Charges

P21S2018 – Connecting Two Conducting Spheres

P21S2018 – Electric Potential of Cylinders

P21S2018 – Electric Potential of Conducting Spheres

P21R2015 – Shooting an Electron

P21B2015 – Electrostatic Analyzer

P21S2014 – One Short of a Hexagon

P21S2013 – Equilibrium of Point Charges

-- CAPACITORS --

Capacitors – Lecture

8 Topics

P22-010 – Capacitors and Capacitance

P22-020 – Parallel-Plate Capacitor

P22-030 – Cylindrical-Plate Capacitor

P22-040 – Spherical-Plate Capacitor

P22-050 – Capacitors in Parallel

P22-060 – Capacitors in Series

P22-070 – Energy Stored in a Capacitor

P22-080 – Effect of a Dielectric Between Capacitor Plates

Capacitors – Problems

11 Topics

P22R2015 – Conceptual Questions About Capacitors

P22L2014 – Ball Hanging Between Parallel Plates

P22R2015 – Electrons & Protons in a Capacitor

P22B2014 – Study of a Parallel Plate Capacitor

P22B2015 – Cylindrical Capacitor

P22B2014 – Spherical Capacitor

P22S2018 – Dielectric Slab & Energy Storage

P22L2014 – Connecting Two Capacitors

P22S2013 – Equivalent Capacitance

P22S2014 – Four Capacitor Network

P22S2012 – Capacitance of a Cap. Network

-- DC CIRCUITS --

DC Circuits – Lecture

15 Topics

P23-010 – Electric Current

P23-020 – Current Density

P23-030 – Drift Velocity

P23-040 – Resistivity and Conductivity

P23-050 – Circuit Component: the resistor

P23-060 – Assembling Resistors in Parallel and Series

P23-070 – Circuit Component: the capacitor

P23-080 – Assembling Capacitors in Parallel and Series

P23-090 – Circuit Component: the battery

P23-100 – Generator Convention & Receptor Convention

P23-110 – Kirchhoff’s Laws

P23-120 – Electric Power

P23-130 – The RC Circuit

P23-140 – Short-Term and Long-Term Behavior

P23-150 – Time Constant of the RC Circuit

DC Circuits – Problems

10 Topics

P23R2015 – Simple Circuit

P23R2016 – Blowing a Fuse

P23R2015 – Equivalent Resistance

P23R2015 – Neither Series nor Parallel

P23R2015 – Behavior of Capacitors

P23S2017 – Resistors & Capacitors

P23B2014 – RC Circuit Behavior

P23B2015 – Equivalent RC Circuit

P23B2021 – RC Circuit

P23R2016 – RC Circuit with a Switch

-- MIDTERM 1 - STUDY GUIDE --

Lowhorn – 8B 2019 Spring – Midterm 1

3 Topics

P19L2019 – Square with Point Charges

P19L2019 – Semicircle with Opposite Densities

P21L2019 – E and V of an Insulating Sphere

Lowhorn – 8B 2020 Spring – Midterm 1

4 Topics

P23L2020 – Circuit with Six Resistors

P23L2020 – Power and Current

P21L2020 – E and V of an Insulating Cylinder

P21L2020 – Distant Point Charges

Lowhorn – 8B 2021 Spring – Midterm 1

4 Topics

P21L2021 – Dipole Field on Axis

P21L2021 – E and V of Concentric Cylinder and Shell

P21L2021 – E and V on Ring Axis

P23L2021 – Asymptotic Behavior of a Circuit

Lowhorn – 8B 2022 Fall – Midterm 1

4 Topics

P21L2022 – Concentric Conductor and Insulator

P21L2022 – Ring with Opposite Densities

P23L2022 – Charging Capacitors Over Time

P23L2022 – Switching in a Battery

-- MAGNETISM --

Magnetism – Lecture

20 Topics

P24-010 – Phenomenon

P24-020 – Magnetic Field & Magnetic Field Lines

P24-030 – Magnetic Field & Symmetry

P24-040 – Principle of Superposition

P24-050 – Reminder: cross product of two vectors

P24-060 – Magnetic Force on a Moving Point Charge

P24-070 – Magnetic Force on a Current

P24-080 – Motion of Charged Particles through B

P24-090 – The Lorentz Force

P24-100 – Biot-Savart Law

P24-110 – Biot-Savart Application: semicircular wire of current

P24-120 – Biot-Savart Application: ring of current

P24-130 – Biot-Savart Application: field on the axis of a ring of current

P24-150 – Ampere’s Law

P24-140 – Biot-Savart Application: finite wire of current

P24-160 – Ampere’s Law: infinite wire of current

P24-170 – Ampere’s Law: infinite slab of current

P24-180 – Ampere’s Law: infinite solenoid

P24-190 – Ampere’s Law: toroid with current

P24-200 – Magnetic Dipole

Magnetism – Problems

16 Topics

P24R2015 – Linear Motion Through E and B

P24B2016 – Mass Spectrometer

P24R2015 – Short Path Through B

P24R2015 – Spiraling Through B

P24S2013 – Traveling Through B

P24S2017 – E and B Fields from an Infinite Wire

P24B2016 – Loop Suspended in a Magnetic Fied

P24B2016 – Magnetic Force on a Current

P24R2015 – Two Parallel Wires

P24R2015 – Force on a Rectangular Loop

P24S2014 – Force on Current-Carrying Wires

P24R2015 – Three Parallel Wires

P24B2014 – Coaxial Cable

P24R2015 – Hollow Cylindrical Conductor

P24R2015 – Slab of Current

P24S2013 – Infinite Hollow Wire

-- INDUCTION --

Induction – Lecture

14 Topics

P25-010 – Phenomenon

P25-020 – Motional EMF: moving rod in a magnetic field

P25-030 – Motional EMF: coil moving through a magnetic field

P25-040 – Magnetic Flux

P25-050 – How Magnetic Flux Varies

P25-060 – Classic Computations of Magnetic Flux

P25-070 – Lenz’s Law

P25-080 – Faraday’s Law

P25-090 – Faraday’s Law: conducting ring in a varying magnetic field

P25-100 – Faraday’s Law: conducting rod on parallel rails

P25-110 – Faraday’s Law: rotating loop in a magnetic field

P25-120 – Mutual Inductance & Self-Inductance

P25-140 – Circuit Component: inductor

P25-150 – Energy Stored in an Inductor

Induction – Problems

11 Topics

P25R2015 – Jumping Ring

P25B2014 – Square Loop and Induction

P25R2016 – Loop Traveling Through B

P25R2015 – Shrinking Loop

P25R2015 – Rod on Rails

P25S2013 – Moving a Rod on Rails

P25S2017 – Rod on Parallel Rails

P25S2018 – Metal Rails in Varying Magnetic Field

P25S2018 – Moving Rod and Two Resistors

P25S2014 – Two Rods on Rails

P25S2021 – Rod Sliding on Triangular Rods

-- ELECTROMAGNETIC WAVES --

EM Waves – Lecture

9 Topics

P27-020 – Maxwell’s Equations

P27-030 – EM Waves

P27-040 – EM Wave Spectrum

P27-050 – Properties of EM Waves

P27-060 – Energy Density of Electric and Magnetic Fields

P27-070 – Poynting Vector and Intensity

P27-080 – Radiation Pressure

P27-090 – Polarization of EM Waves

P27-100 – Malus’s Law

EM Waves – Problems

11 Topics

P27B2014 – Electromagnetic Wave

P27B2014 – EM Waves Questions

P27B2022 – Intensity of a Plane EM Wave

P27B2023 – Fields of an EM Wave

P27R2015 – Radio Antenna

P27R2016 – Electromagnetic Wave

P27B2020 – Plane EM Wave in Vacuum

P27R2015 – Two Polarizers in Series

P27R2015 – Three Polarizers in Series

P27R2015 – Optimizing Three Polarizers

P27R2017 – Laser and Polarizers

-- OPTICS --

Optics – Lecture

28 Topics

P28-010 – Linear Propagation of Light and the Ray Model

P28-020 – Index of Refraction

P28-030 – Change in Medium

P28-040 – Dispersion

P28-050 – Law of Reflection

P28-060 – Refraction & Snell’s Law

P28-070 – Total Internal Reflection

P28-080 – Brewster’s Law

P28-090 – Object Distance, Image Distance, Real & Virtual Images

P28-100 – Magnification

P28-110 – Plane Mirrors & Ray Tracing

P28-120 – Spherical Mirrors

P28-130 – Ray Tracing Rules for Spherical Mirrors

P28-140 – Principal Rays for Concave Mirrors

P28-150 – Principal Rays for Convex Mirrors

P28-160 – Mirror Equation

P28-170 – Magnification of Spherical Mirrors

P28-180 – Thin Lenses

P28-190 – Ray Tracing Rules for Thin Lenses

P28-200 – Principal Rays for Converging Lenses

P28-210 – Principal Rays for Diverging Lenses

P28-220 – Lens Equation

P28-230 – Magnification for Thin Lenses

P28-240 – Assembling Two Lenses Together

P28-260 – Images Formed by Refracting Surfaces

P28-270 – The Lensmaker’s Equation

P28-280 – The Human Eye

P28-290 – The Magnifying Glass

Optics – Problems

20 Topics

P28R2015 – Reflections Off of a Corner Mirror

P28R2015 – Fishing and Optics

P28B2014 – Optical Fiber

P28S2013 – Reflection and Refraction in a Slab

P28S2018 – Refraction in a Sphere

P28R2015 – Reflection & Refraction in a Prism

P28R2015 – Total Internal Reflection

P28R2016 – Flashlight and Swimming Pool

P28R2017 – Three Slabs of Transparent Media

P28R2015 – Concave Mirror

P28R2015 – Diverging Lens

P28R2015 – Myopic Biologist

P28R2015 – Vision Defect in the Human Eye

P28R2015 – Finding the Object from the Image

P28S2013 – Mobile Converging Lens

P28R2015 – Combining a DV Lens and a CV Lens

P28R2015 – Combining a DV Lens and a CV Mirror

P28S2014 – Combining Two Lenses

P28R2015 – Two Lenses

P28S2018 – Half-Silvered Lens

-- MIDTERM 2 - STUDY GUIDE --

Lowhorn – 8B 2019 Spring – Midterm 2

4 Topics

P23L2019 – Equivalent Resistance

P23L2019 – Unknown Battery Voltage

P24L2019 – Magnetic Force on a Bent Wire

P24L2019 – Wires with Opposite Currents

Lowhorn – 8B 2020 Spring – Midterm 2

3 Topics

P24L2020 – Bent Wire of Current

P24L2020 – Pair of Infinite Wires

P25L2020 – Flux Through a Loop

Lowhorn – 8B 2021 Fall – Midterm 2

4 Topics

P28L2021 – Reflection Refraction and EM Waves

P24L2021 – Semicircles of Current

P25L2021 – Loop Falling Through B

P24L2021 – Coaxial Cable

Lowhorn – 8B 2022 Fall – Midterm 2

4 Topics

P24L2022 – Current-Carrying wire and Shell

P25L2022 – Flux and Induced Current

P28L2022 – Pool Light

P28L2022 – DV Mirror and Lens

-- INTERFERENCE & DIFFRACTION --

Interf & Diffraction – Lecture

14 Topics

P29-001 – Principle of Superposition

P29-002 – Constructive & Destructive Interference

P29-003 – Conditions for Constructive & Destructive Interference

P29-010 – Coherent Source

P29-020 – Huygens Principle

P29-030 – Double-Slit Interference: Young’s experiment

P29-040 – Phase Shift Upon Reflection

P29-050 – Thin-Film Interference

P29-060 – Diffraction Condition

P29-070 – Single-Slit Diffraction

P29-080 – Double-Slit Diffraction

P29-090 – Diffraction Grating

P29-100 – Diffraction by a Circular Aperture

P29-110 – Rayleigh’s Criterion

Interf & Diffraction – Problems

12 Topics

P29R2015 – Red Light, Blue Light

P29R2015 – Delaying Light

P29R2015 – Thin Soap Film

P29R2017 – Of Thin Films

P29R2015 – Wedge Interferometry

P29S2013 – Thinning Soap Film

P29S2017 – Observing a Thin Oil Layer

P29B2009 – Alien Skin Interference

P29B2015 – Airy Disk

P29S2013 – Double Slit Interference in Different Media

P29S2017 – Diffraction in Air and in Fluid

P29R2015 – Christmas Lights

-- QUANTUM PHYSICS --

Quantum – Lecture

11 Topics

P31-010 – The Photoelectric Effect

P31-040 – Line Spectra & Energy Levels

P31-050 – Bohr’s Model of the Hydrogen Atom

P31-060 – Bohr Radii

P31-070 – Energy Levels of the Hydrogen Atom

P31-080 – Balmer’s Formula for the Hydrogen Spectrum

P31-090 – Bohr’s Model for Hydrogen-like Atoms

P31-110 – Electron Diffraction & de Broglie Wavelength

P31-120 – The Heisenberg Uncertainty Principle

P31-130 – Schrödinger’s Equation & Wavefunctions

P31-140 – Infinite Potential Well: the “particle in a box”

Quantum – Problems

16 Topics

P31R2015 – About the Photoelectric Effect

P31R2016 – The Photoelectric Effect

P31R2015 – Photoelectric Effect in Cs & Al

P31R2017 – Mysterious Metal and Photoelectric Effect

P31R2015 – Excited States of Hydrogen

P31J2009 – Finding Energy Levels Experimentally

P31R2015 – Kinetic Energy of Particles

P31R2015 – Sunlight & Photons

P29R2015 – Double Slit Interference with Electrons

P31S2013 – Single-Slit Diffraction with Electrons

P31B2009 – Miscellaneous Quantum Questions

P31B2014 – Electron in an Infinite Potential Well

P31B2015 – Infinite Potential Well with an Electron

P31B2009 – Alien Vision

P31B2014 – Finite Potential Well

P31B2020 – Excited Particle in a Potential Well

-- FINAL - STUDY GUIDE --

Lowhorn – 8B 2019 Spring – Final

5 Topics

P28L2019 – One Image or Two

P32L2019 – Contracted Denebian Starship

P29L2019 – From Bright to Dark Fringe

P21L2019 – Nested Spherical Shells

P23L2019 – Circuit with Multiple Resistors

Lowhorn – 8B 2020 Spring – Final

4 Topics

P24L2020 – Two Semicircular Wires

P32L2020 – Relativistic Rabbit

P28L2020 – Unknown Lens

P21L2020 – E and V of a Wire in a Shell

Lowhorn – 8B 2021 Fall – Final

6 Topics

P31L2021 – Four Polarizers and Photoelectrons

P29L2021 – Double Slit Diffraction Pattern

P28L2021 – Conditions on Image Formation

P25L2021 – Magnetic Field from a Circuit

P21L2021 – E and V of Concentric Sphere

P31L2021 – Quantum

Multiple Choice

9 Topics

Buehler – 8B 2011 Summer – Multiple Choice

Buehler – 8B 2014 Summer – Multiple Choice

Buehler – 8B 2015 Summer – Multiple Choice

Buehler – 8B 2016 Summer – Multiple Choice

Buehler – 8B 2018 Summer – Multiple Choice

Buehler – 8B 2019 Summer – Multiple Choice

Buehler – 8B 2020 Summer – Multiple Choice (1 of 3)

Buehler – 8B 2020 Summer – Multiple Choice (2 of 3)

Buehler – 8B 2020 Summer – Multiple Choice (3 of 3)

P19-040 – Principle of Superposition

Physics 8B – Fall 2024 (Barsky) Electric Fields – Lecture P19-040 – Principle of Superposition

Principle of superposition:

The net electric field at any point is equal to the vector sum of the respective electric fields that each charge distribution would create on its own.

\boxed{\overrightarrow{E}_{net}=\overrightarrow{E}_{1}+\overrightarrow{E}_{2}+\overrightarrow{E}_{3}+\dots}

Example:

The net electric field ${\overrightarrow{E}}_{net}$ at point $P$ is equal to the vector sum of the individual electric fields ${\overrightarrow{E}}_1$ and ${\overrightarrow{E}}_2$ created by point charges $q_1$ and $q_2$ respectively. Thus, we write

\boxed{{\overrightarrow{E}}_{net}={\overrightarrow{E}}_1+{\overrightarrow{E}}_2}

In practice, since the above equation is the sum of two vectors, we write it in component form as follows

\begin{aligned} {\overrightarrow{E}}_{net}={\overrightarrow{E}}_1+{\overrightarrow{E}}_2\ \ \ \ &\Rightarrow \ \ \ \ \ \left\{ \begin{array}{c} E_{net\ x}=E_{1x}+E_{2x} \\ E_{net\ y}=E_{1y}+E_{2y} \end{array} \right. \\ \\ &\Rightarrow \ \ \ \ \ \left\{ \begin{array}{c} E_{net\ x}=E_1{\mathrm{cos} \left({\theta }_1\right)\ }+E_2{\mathrm{cos} \left({\theta }_2\right)\ } \\ E_{net\ y}=E_1{\mathrm{sin} \left({\theta }_1\right)\ }-E_2{\mathrm{sin} \left({\theta }_2\right)\ } \end{array} \right. \end{aligned}

The magnitude of the net electric field at point $P$ is therefore equal to

E_{net}=\sqrt{E^2_{net\ x}+E^2_{net\ y}}=\sqrt{{\left(E_1{\mathrm{cos} \left({\theta }_1\right)\ }+E_2{\mathrm{cos} \left({\theta }_2\right)\ }\right)}^2+{\left(E_1{\mathrm{sin} \left({\theta }_1\right)\ }-E_2{\mathrm{sin} \left({\theta }_2\right)\ }\right)}^2}