*Note: this material may be taught in first or second semester physics, depending on the school.

Waves and Waves on a String

• *Frequency, wavelength, amplitude and wave speed.
• *Tension, linear density and wave speed on a string + example.
• *Fixed and free reflections, superposition principle., constructive/destructive interference.
• *Resonance for a string clamped at both ends + driving at a resonant frequency.
• *Example:  another resonance example for a string - many frequencies superposed.
• *Example:  resonance on a string, find the 2nd harmonic based on the 3rd harmonic.
• *Example:  wave speed and tension given the linear density and frequency of the 5th harmonic.
• *Example:  given two normal modes on a string, compute the fundamental harmonic, wave speed and tension.

Wave Animations

• *Animation: Transverse and Longitudinal Waves
• *Animation: Waves on the surface of water (a combination of transverse and longitudinal)
• *Animation:  Waves on the surface of water (peakedness depends on amplitude of circular motion)
• *Animation:  Rayleigh waves in a solid (seismic waves on a surface).
• *Animation: Wave reflections:  fixed end vs. free end, fast to slow transitions vs. slow to fast transitions.
• *Animation: Constructive and destructive interference, and formation of standing waves on a string.
• *Animation: Standing waves on a guitar string and superposition of normal modes.

*Note: this material may be taught in first or second semester physics, depending on the school.

Waves and Waves on a String

• The wave function for a wave traveling on a string [2023.01.20]
• Derivation of the 1D wave equation using partial derivatives of the wave function [2023.01.21]
• Derivation of the wave equation using Newton's 2nd law + formula for speed [2023.01.22]
• Wave function for a standing wave, boundary conditions and normal modes on a string of length L [2023.01.24]
• Energy transmitted by a wave on a string [2025.01.18]
• Potential and kinetic energy in a wave [TBA]

Introduction to Sound and Resonance with Sound

• Quick review of elastic moduli:  Young's Modulus and Bulk Modulus [2025.01.19]
• Longitudinal waves: essential concepts for sound waves [2025.01.19]
• Deriving the pressure wave function, relation between pressure and displacement amplitudes [2025.01.20]
• The speed of sound in bulk materials, thin rods and gases [TBA]
• Standing waves and normal modes for sound in an air column [TBA]

Animations

• *Animation: Math lesson: how to make a wave move to the left and right. [2021.10.02]
• *Animation: Motion perpendicular to the direction of wave velocity:  time derivatives of the wave function [2023.01.21]
• *Animation: Wave reflections:  fixed end vs. free end, fast to slow transitions vs. slow to fast transitions. (review)
• *Animation: Constructive and destructive interference, and formation of standing waves on a string. (review)

*Note: this material may be taught in first or second semester physics, depending on the school.

Energy and Intensity for Sound Waves:

• *Energy and intensity for sound waves, and the decibel (dB) scale [2025.01.25]
• *The Decibel scale and related calculations [2025.01.26]

Doppler Effect, Interference and Shock Waves:

• *The Doppler effect, derivation of equations + examples [2023.01.31]
• *Spatial interference of sound waves:  in class demonstration.
• *Time interference of sound waves:  Acoustic beats and beat frequency [2025.01.24]
• *Shock waves, the sonic boom and the angle of a shock wave + example [2025.02.08]

Animations:

• *Animation:  plane traveling at Mach 2.0 [2025.02.08]
• *Animation:  plane traveling at Mach 1.2 [2025.02.07]
• *Animation:  plane traveling at Mach 1.0 [2025.02.07]
• *Animation:  plane traveling at Mach 0.8 [2025.02.07]
• *Animation:  Beats illustration: overlapping waves arriving at the ear + composite wave arriving at the ear.  [2025.01.25]
• *Animation:  Doppler effect for a stationary source and moving listener [2023.01.29]
• *Animation:  Doppler effect for a moving source and stationary listener [2023.01.29]
• *Animation:  Sound wave interference:  acoustic beats. [2021.10.19]
• *Animation:  The sound barrier, shock waves and sonic booms [2023.02.04]
• *Animation:  spatial interference of light waves (sound is totally analogous if two speakers emit a tone!) [2021.08.03]

Exams and video solutions (2024 - present) will be provided here [TBA]

There will be little quirks here and there, and this week one of those quirks is that we use a "k" for the electric constant in Coulomb's Law in non-calculus physics, but in calculus-based physics we'll use 1/(4*pi*epsilon_0) instead of k, where epsilon_0 is called "the electric constant" or "the permittivity of free space".

Quick Introduction to Coulomb's law and Electric Field (non-calculus intro)

• *Introduction to charge and units of charge. [2021.01.23]
• *The force between charges:  Coulomb's Law [2021.01.24]
•  *Example:  comparison of electric and gravitational forces within the hydrogen atom. [2023.07.31]
• *Example:  Uniform circular motion with Coulomb's Law [2021.01.24]
• *Introduction to electric field, electric field of a point charge, and force exerted by the electric field. [2021.01.24]
• *Example:  Electron accelerated by the uniform electric field in a parallel plate capacitor. [2021.01.24]
• *Example:  Vector addition for sketching the electric field of a dipole. [2021.01.25]
• *Example:  Deflection of an electron shot between charged plates. [2021.01.25]
• *Example:  Three point charges, field and forces [TBA]

Additional Topics for PHYS7:

• *Example:  E-field of a uniformly charged rod, observation point on the rod axis (physical integration) [2023.07.24]
• *Example: E-field due to a line of charge, observation point on the perpendicular bisector (physical integration). [2023.02.07]
• *Example:  E-field due to a half-ring of charge (physical integration) [2023.08.28]
• *Introduction to electric dipoles, and calculation of field strength on the axis of a dipole + binomial approximation [2024.02.15]
• *Torque and potential energy for a dipole in a uniform electric field [2024.02.17]
• *Example:  alternative video for field of a dipole on axis (accidentally covered this twice!) [2023.09.04]
• *Example:  electric field due to a finite rectangular sheet by breaking into thin finite rods [TBA]

Animations:

• *Electric dipole oscillating in a uniform electric field [2024.02.18]
• *Zooming in on the dipole field starting from the asymptotic field (large distance approximation) [2024.02.18]

Review Material - Introduction to Vectors:

• *Introduction to vectors and geometric vector addition. [2021.08.21]
• *Vector components introduction and examples. [2021.08.21]
• *Quantitative vector addition using components [2021.08.22] 
• *Vector algebra:  scalar multiples, unit vectors, components [2021.08.23]
• *Vector algebra:  vector opposites, zero vector, vector subtraction [2021.08.23]
• *Vector algebra:  dot product, geometric and algebraic views [2021.08.23]

Electric Flux and Applications of Gauss' Law

• *Derivation of electric flux and Gauss' Law + example of a charged shell [2023.02.21]
• *Example:  electric field of a line charge using Gauss' Law [2023.02.22]
• *Example:  electric field of a sheet of charge using Gauss' Law [2023.02.23]
• *Example:  electric field of a uniformly charged sphere using Gauss' Law [2023.02.24]
• *Example:  electric field in the cylindrical shell capacitor. [2023.06.11]
• *Example:  electric field in the spherical capacitor. [2023.07.03]

Properties of Conductors

• Properties of Conductors by using Gauss' Law [2025.02.22]

Review of Work and Energy concepts

• *Energy review part 1:  work integral for the work done by a varying force [2020.10.06]
• *Energy review part 2:  where does the formula for kinetic energy come from?  [2020.10.06]
• *Energy review part 3:  path independence of the work done by gravity [2020.10.06]
• *Energy review part 4:  generalizing to work as a line integral [2020.10.06]
• *Energy review part 5:  work done by gravity and gravitational potential energy [2020.10.11]
• *Energy review part 6:  quick proof of conservation of energy [2020.10.11]

Introduction to potential energy and potential with point charges (lite non-calculus intro)

• *Electric potential energy between two charges. [2021.01.25]
• *Introduction to electric potential.[2021.01.25]
• * Review example:  two source charges and a test charge:  force, field, potential energy and potential. [2021.01.25]
• *Example:  Nitrogen-14 atom accelerated through a known potential difference. [2021.03.20]
• *Example:  electron accelerated between charged plates, final speed using potential and energy conservation. [2021.01.27]

Introduction to Electric Potential Energy and Electric Potential (additional calculus-based intro)

• *Review of potential energy, electric potential energy, application to uniform fields and point charge potential energies [2023.03.15]
• *Introduction to electric potential, potential as the path integral of electric field + examples of parallel plate capacitor and charged sphere. [2023.03.17]
• *Electric potential for point charges and extension to continuous distributions of charge + example of the potential due to a ring of charge. [2023.03.18]
• *Finding electric field from the gradient of the potential function [2025.02.28] (not linked to cquiz)
• *Electric field is perpendicular to the equipotential curves [2025.03.01] (not linked to cquiz)
• *Conductors are an equipotential (in electrostatics) [2025.03.01] (not linked to cquiz)

Additional Examples (past quiz and test items)

• *Electric potential on the axis of a uniformly charged rod [2025.03.12]

Capacitance and Dielectrics (Non-Calculus Intro)

•  *Calculating the electric field in a capacitor using potential difference and gap width. [2021.01.30]
•  *Definition and units of capacitance + basic example. [2021.01.31]
•  *Capacitors in series and parallel combinations + examples. [2021.01.31]
•  *The geometry of capacitance:  plate area and gap width used to calculate capacitance. [2021.01.31]
•  *Energy stored in a capacitor (NOTE:  derivation part uses a little bit of calculus). [2021.02.01]
•  *The effects of a dielectric between the plates of a capacitor. [2021.02.02]
•  *Example:  dielectric introduced to a capacitor connected to a battery [2021.02.02]

Capacitance, Dielectrics, Electric Field Energy Density (Calculus-Based Intro)

• *Introduction to capacitance and derivation of the parallel plate capacitance [2023.03.08] 
• *Example:  capacitance of the spherical shell capacitor. [2023.07.10] 
• *Electric field energy density using the parallel plate capacitor (formula generalizes to other cases) [2023.06.08]
• *Example:  energy in the spherical shell capacitor two different ways [2023.07.07] 
• *Dielectrics, surface charge density, permittivity and electric field in the presence of a dielectric. [2025.03.03]need to link to cquiz
• *Electric field energy density in the presence of a dielectric [2025.03.07] (not linked to cquiz)
• *Gauss' Law with dielectrics + spherical capacitor with a dielectric. [2025.03.08] (not linked to cquiz)

Additional Examples:

• *Example: capacitors in series and parallel, max and min capacitance [2022.03.06]
• *Example: Charge and energy on a capacitor, required area to build the capacitor. [2022.02.08]
• *Example:  foil and paper capacitor rolled up:  capacitance, charge and energy. [2022.01.27]
• *Example:  capacitance, charge and energy for a capacitor. [2021.02.08]

Exams and video solutions (2024 - present) will be provided here [TBA]

Current and Resistance (non-calculus level intro):

•  *Definition of current + basic example, meaning of area under a current-time graph. [2021.02.01]
•  *Derivation of drift velocity [2021.02.02]
•  *The geometry of resistance:  dependence on length and cross section. [2021.02.08]
• *Ohm's Law:  motivation, graphical representation and lab demonstration. [2021.02.08] 
•  *Temperature dependence of resistance + example. [2021.02.09]
•  *Power dissipated by a resistor + examples. [2021.02.04]
• *Internal resistance and the terminal voltage of a power source. [2021.02.09]
•  *Example:  current, charge and power in a simple circuit. [2021.02.07] 
  
  

Current and Resistance (calculus-based/advanced level intro):

Note: will develop videos based on lecture notes for these topics!

•  *Drift velocity: physics simulation and derivation of drift velocity formula [TBA]
•  *Ohm's law in terms of electric field and current density [TBA]
•  *Derivation of resistance of a conductor [TBA]
•  *A note on power input and output for ANY circuit element [TBA]
•  *Basic complete circuit concepts/water flow analogies [TBA]
•  *Steady state resistor-capacitor concept circuits [TBA]
•  *Circuit analysis for charging a battery?  Power in vs. power out clarification [TBA]

Resistor Networks and Kirchhoff's Laws:

•  *Resistors in series and parallel + examples. [2021.02.05]
•  *Example:  simplifying resistor networks 1. [2021.02.07]
•  *Example:  simplifying resistor networks 2. [2021.02.07] 
•  *Example:  simplifying resistor networks 3. [2021.02.25]
•  *Example:  node voltages in a three resistor circuit lab demo (this is Part 1 of the lab!) [2021.02.13]
•  *Introduction to the galvanometer and constructing ammeters and voltmeters. [2021.02.14] 
•  *Introduction to Kirchoff's laws and example using a CAS to solve for the branch currents. [2021.02.12]
•  *Another Kirchoff example with CAS and an internal dependency in the system of equations. [2021.02.13]
•  *Another Kirchoff example using a CAS to solve six equations and six unknowns. [2021.02.25]

Additional Examples:

• *Example: kirchoff circuit with 5 branch currents [2022.03.20]
• *Example: ammeter design [2022.02.18]
• *Example:  resistor network with parallel and series, current, power. [2022.01.29]
• *Example:  resistor network with series and parallel, current, terminal voltage, power. [2022.01.27]
• *Another Kirchoff example: two power sources, six branches, CAS used to solve the system. [2022.01.28]
• *Another Kirchoff example: two power sources, six branches, CAS used to solve the system. [2022.01.28]
• *Example:  total resistance and power dissipated in a string of Christmas lights. [2021.03.20]

Introduction to Magnetic Forces and Fields (non-calculus level intro):

• *Introduction to magnets and magnetic fields. [2021.02.27]
• *The Lorentz force law and right-hand rules + examples. [2021.02.22]
• *The velocity selector + examples. [2021.02.23]
• *The Hall effect and Hall probe example. [2021.02.23]
• *Cyclotron motion + example. [2021.02.23]
• *The Bainbridge mass spectrometer + example. [2021.02.24]
• *Force on a current carrying wire in a magnetic field. [2021.03.01]
• *Torque on a current loop and the basics of electric motors. [2021.03.01]

Introduction to Magnetic Forces and Fields (calculus-based/advanced level):

Note: will develop these videos from lecture notes!

• Magnetic field lines and magnetic flux. + "Gauss Law for magnetism" [TBA]
• Generalized Lorentz force law. [TBA]
• Magnetic moments and additional bar magnet discussion. [TBA]
• Thompson's e/m experiment and Millikan's oil drop experiment [TBA]
• Possible additional DC motor calculations. [TBA]
• Hall effect written in terms of current density. [TBA]

Additional Examples:

• *Example: RC circuit example (relevant to lab). [2022.01.31]
• *Example: Lorentz force concept questions [2022.03.20]
• *Example:  N-14 accelerating potential and magnetic field in the analyzer region of a mass spectrometer. [2022.02.04]
• *Example:  solar wind electron in cyclotron motion about the Earth's magnetic field. [2022.02.04]

The Biot-Savart Law and Applications:

• *Magnetic field of a moving charge and example of magnetic force between two charges [2024.05.03]
• *The Biot-Savart law and example of B-field of a straight conductor [2024.05.04]
• *Magnetic field of a circular current loop or a flat coil using Biot-Savart  [2024.05.07]
• *Direct calculation of the magnetic field at the center of a ring using Biot-Savart [2024.05.10]
• *Magnetic field at the center of a rotating ring of charge [2024.08.17]

Ampere's Law and Applications:

• *Informal derivation of Ampere's Law. [2024.05.31]
• *long straight wire using Ampere's Law (logically circular, but makes a quick example) [2024.06.04]
• *long cylindrical conductor using Ampere's Law [2024.06.18]
• *B field of a solenoid using Ampere's Law [2024.07.24]
• *B field of a toroid using Ampere's Law [2024.07.31]

Exams and video solutions (2024 - present) will be provided here [TBA]

Electromagnetic Induction (non-calculus intro):

• *Introduction to electromagnetic induction and Lenz's Law [2021.03.09]
• *Faraday's Law:  induced EMF [2021.03.09]
• *Electric generators and the generator formula [2021.03.09]
• *Motional EMF (from first problem solving set). [2021.03.10]
• *Example:  rotating coil in the Earth's magnetic field. [2021.03.10]
• *Example:  Lenz's law one coil induces current in another. [2021.03.10]
• *Example:  more qualitative examples of induced current in coils. [2022.02.11]
• *Self-Inductance of a solenoid. [2021.03.15] (included here to time with inductance lab)

Electromagnetic Induction and Completing Maxwell's Equations (calculus-based physics):

These and other video topics will be developed from my lecture notes!

• Back EMF derivation. [TBA}
• Slidewire generator, including work and power considerations. [TBA]
• Induced electric field. [TBA]
• Displacement current and summarizing Maxwell's equations. [TBA]

Self inductance (non calculus level):

• *Self-Inductance of a solenoid. [2021.03.15] 
• *Introduction to RL circuits, inductors and back EMF [2022.03.15]
• *RL circuit oscilloscope demo [2022.03.15]

Mutual Inductance, Self Inductance and B-field energy density (calculus-based):

These and other video topics will be developed from my lecture notes!

• *Introduction to mutual inductance + example of nested coils [TBA]
• *Derivation of self inductance for a solenoid (redo of video above) [TBA]
• *Energy in an inductor [TBA]
• *Derivation of magnetic field energy density using a solenoid [TBA]
• *Example:  self-inductance of a coaxial cable [TBA]

AC Circuits and Phasor Analysis:

• *Intro AC circuits:  the current phasor and resistor voltage phasor [2025.04.07]
• *The inductor voltage phasor and inductive reactance [2025.04.08]
• *The capacitor voltage phasor and capacitive reactance [2025.04.08]
• *RMS values for current and voltage - full calculus derivation [2025.04.19]
• *RLC series circuit phasor analysis:  finding the source voltage, impedance and phase angle [2025.04.11]
• *Power in AC circuit elements:  resistors, inductors and capacitors [2025.04.27]
• *Power and the power factor in the RLC series circuit [2025.05.05]
• *Resonance in the RLC series cicuit [TBA]

This section is TBA - will develop proper material on derivation of the wave equation for EM waves in addition to basic wave properties, etc. For now, here is a very brief overview of EM waves that I use in my non-calculus physics courses:

• *Introduction to electromagnetic waves [2021.03.23]