Calculus-Based Physics II - Master Video List
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Module 1: Brief Introduction to Mechanical Waves
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.
Module 2: One-Dimensional Wave Equation, Sound Intro
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)
Module 3: Additional Topics in Sound and Hearing
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]
Module 4: Modules 1–3 Exam
Note: Recent exams and solutions (2025-present) will appear in this space. [TBA]
Module 5: Charge and Electric Field
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 Electric Field Topics and Dipoles (calculus-based physics)
- 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]
Module 6: Electric Flux and Gauss' Law
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
Module 7: Electric Potential
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)
Module 8: Capacitance and Dielectrics
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]
- 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]
Module 9: Modules 5–8 Exam
Note: Recent exams and solutions (2025-present) will appear in this space. [TBA]
Module 10: Current, Resistance and Simple Circuits
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)
- 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]
Module 11: More DC Circuits and Kirchhoff's Laws
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]
Module 12: Magnetic Field and Magnetic Force
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)
- 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]
Module 13: Sources of Magnetic Field, Biot-Savart Law, Ampere's Law
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]
Module 14: Modules 10–13 Exam
Note: Recent exams and solutions (2025-present) will appear in this space. [TBA]
Module 15: Electromagnetic Induction, Faraday's Law and Transformers
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]
Electromagnetic Induction and Completing Maxwell's Equations (calculus-based physics)
- Back EMF derivation. [TBA}
- Slidewire generator, including work and power considerations. [TBA]
- Induced electric field. [TBA]
- Displacement current and summarizing Maxwell's equations. [TBA]
Module 16: Inductance and RL Circuits
Self inductance (non calculus level)
- Self-Inductance of a solenoid. [2021.03.15]
- Introduction to RL circuits, inductors and back EMF
- RL circuit oscilloscope demo
Mutual Inductance, Self Inductance and B-field energy density (calculus-based)
- 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]
Module 17: AC Circuits and Phasor Analysis
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]