Deep Physics: Electricity and Magnetism for Talented High Schoolers
Real electricity and magnetism, taught from Coulomb’s law through fields, circuits, magnetic forces, and induction. For talented high schoolers.
Online for homeschool families anywhere · or in-person in Princeton, NJ
A World Through the Lens of Electricity and Magnetism
Almost everything in modern technology, from the spark of a battery to the light from the Sun, is one phenomenon. Electricity and magnetism are two sides of it.
Rub a balloon on your hair and press it to a wall. It sticks. Friction transferred a few electrons, and the resulting force holds the balloon up against gravity.
Lay a magnet on a table next to a wire. Switch on the current. The wire jumps. The same charges in the wire feel a force that did not exist a moment earlier.
Drop a strong magnet through a copper tube. It falls in slow motion. No friction touches the walls. The currents the magnet induces in the tube push back on it.
Plug your laptop charger into the wall. The brick has no moving parts. The voltage going in is different from the voltage coming out. Two coils share one changing magnetic field.
Electricity and magnetism look like two separate subjects. They are not. A static charge and a moving charge interact through fields that are themselves linked: a changing magnetic field makes an electric field, a moving charge makes a magnetic field. The same set of laws describes a battery, a transformer, an antenna, and the light from the Sun.
You will:
- Compute the electric field and potential of a simple charge configuration from Coulomb’s law and superposition.
- Apply Gauss’s law to use symmetry on problems no direct calculation could touch.
- Solve any DC circuit with Kirchhoff’s two laws and Ohm’s law.
- Use Faraday’s and Lenz’s laws to predict the EMF induced by a changing magnetic flux, and the direction of the induced current.
What You Will Actually Understand
1. Electric Charge and Coulomb’s Law
Where electromagnetism starts. Electric charge as a fundamental property of matter. Conservation and quantization of charge. Coulomb’s law as the inverse-square force between point charges. Superposition: the field of many charges as the sum of individual fields.
2. Electric Fields and Potential
From a force on a test charge to a field everywhere. The electric field as force per unit charge. Field lines and what they encode. Electric potential and its connection to the field. Gauss’s law as a symmetry tool that bypasses direct integration.
3. Capacitance and Dielectrics
Storing energy in an electric field. Capacitance as charge per voltage. The parallel-plate capacitor. Dielectrics and how they boost capacitance. Energy stored in a charged capacitor, written as energy stored in the field itself.
4. Current, Resistance, and Conduction in Various Media
From a microscopic drift of electrons to the transistor. Electric current as charge in motion. Resistance, resistivity, and Ohm’s law. EMF, batteries, internal resistance. Kirchhoff’s two laws for any DC network. Conduction in different media: the Drude picture in metals, a glance at superconductivity, current in electrolytes and in gases, conduction in vacuum, and semiconductors with the p–n junction and the transistor at the end.
5. Magnetic Fields, Forces, and Magnetic Materials
What happens when charges start to move, and how matter responds to the field they make. The magnetic field. The Lorentz force on a moving charge. Force on a current-carrying wire and torque on a current loop. Sources of magnetic field: a long straight wire, a solenoid, and the laws (Biot–Savart, Ampère) behind them. Magnetic materials: diamagnetism, paramagnetism, ferromagnetism. No magnetic monopoles: the statement, parallel in form to Gauss’s law for E but opposite in content, that the magnetic flux through any closed surface vanishes. One of Maxwell’s four equations.
6. Electromagnetic Induction and AC Circuits
A changing magnetic field makes an electric field, and the circuits and waves that follow from it. Induction. Magnetic flux. Faraday’s law of induction. Lenz’s law and the direction of the induced current. Self- and mutual inductance. Energy stored in a magnetic field, alongside the energy already stored in an electric field. AC circuits. The LC oscillator as the electromagnetic harmonic oscillator, with the same period equation as a mass on a spring. Alternating current, with inductive and capacitive reactance and the phase shift each one introduces. Resonance in a series RCL circuit. AC power, RMS values, and the transformer. Maxwell’s equations and light. Maxwell’s displacement current, completing the four equations of electromagnetism. Electromagnetic waves at speed c, and light as one of them.
The specific topics, and the depth given to each, may shift depending on class priorities and the dynamics of the cohort.
Schedule, Pricing & Enrollment
Formats: Fall, Spring, and Summer semesters.
Schedule, format, tuition, refund policy, and certificates apply to every Lyceum course. They live on the Physics Lyceum: High School overview.
To enroll, schedule a call. We confirm fit, prerequisites, and the right semester.
Part of the SoTS Physics Lyceum
Electricity and Magnetism is one of six classical core courses in the SoTS Physics Lyceum: a multi-year curriculum in Princeton, NJ. Students earning the Mastery in Classical and Modern Physics complete the six classical core courses plus any two of the four modern electives.
Classical core: Mechanics of motion. Mechanics of bodies and fluids. Waves and oscillations. Thermodynamics. Electricity and magnetism. Geometric optics.
Modern electives: Special Relativity. Quantum mechanics. Nuclear and particle physics. Astronomy and cosmology.
The Lyceum is built on the Deep Physics methodology.