⚡ Electricity & Magnetism
Charges, fields, currents and circuits. From Coulomb's law and Ohm's law to magnetism and electromagnetic induction.
What you will learn
- Calculate forces between charges with Coulomb's law
- Analyze series and parallel circuits with Ohm's law
- Apply Kirchhoff's laws to multi-loop circuits
- Explain electromagnetic induction with Faraday's law
Study guide
High School concepts
AC Basics — Sine Waves, Frequency and RMS Voltage
Alternating current basics: the sine wave, frequency and period, peak vs RMS voltage (why 120 V mains peaks at 170 V), and how resistors, capacitors and…
Coulomb's Law — F = kq₁q₂/r² Explained
Coulomb's law: the force between electric charges. Inverse-square law, the constant k, and worked examples with unit checks.
Electric Field — E = F/q, Field Lines and Worked Examples
The electric field: force per unit charge. Field lines, uniform fields, E = F/q and E = kQ/r², with worked examples.
Magnetic Force — F = qvB, Direction and Circular Motion
Magnetic force on moving charges and currents: F = qvB sinθ and F = ILB sinθ, the right-hand rule, why magnetic forces do no work, and circular motion in a…
Magnetism Basics — Fields, Poles and the Right-Hand Rule
Magnetism: poles, magnetic fields, fields from currents, the force on moving charges (F = qvB), and the right-hand rule.
Ohm's Law — V = IR Explained with Circuits and Examples
Ohm's law V = IR: voltage, current and resistance. What each means, when the law holds, and worked circuit examples.
Series vs Parallel Circuits — Rules, Formulas and Examples
Series and parallel circuits: how current and voltage split, equivalent resistance formulas, and worked examples with two bulbs.
Introductory College concepts
Capacitance in Detail — C = Q/V, Energy and Combinations
Capacitance in depth: C = Q/V, the parallel-plate formula C = ε₀A/d, dielectrics, energy U = ½CV², and series/parallel combinations with a worked example.
Electric Potential (Voltage) Explained — V = W/q
What voltage really means: electric potential energy per unit charge, V = W/q, equipotentials, and how voltage drives current through a circuit.
Faraday's Law of Induction — How Changing Magnetism Makes Electricity
Faraday's law: changing magnetic flux induces EMF. EMF = −NΔΦ/Δt, Lenz's law, magnetic flux, and how generators work.
Kirchhoff's Laws — KCL and KVL with Worked Examples
Kirchhoff's current and voltage laws: conservation of charge and energy in circuits. Rules, sign conventions, and a worked multi-loop example.
Beginner concepts
Electric Charge — The Basics: Positive, Negative and Conservation
Electric charge: what it is, positive and negative, conductors vs insulators, charging methods, and conservation of charge.
The Electromagnetic Spectrum — From Radio to Gamma Rays
The electromagnetic spectrum from radio waves to gamma rays: what unites all EM waves, how frequency, wavelength and photon energy relate, and what each…
Intermediate concepts
Lenz's Law — Why Induced Current Opposes Change
Lenz's law: why induced current always opposes the change in magnetic flux, how it enforces energy conservation, eddy currents, and worked flux-change examples.
RC Circuits — Time Constant, Charging and Discharging
RC circuits explained: the time constant τ = RC, exponential charging and discharging curves, why a capacitor blocks DC in steady state, and a worked timing…
Formulas
C = Q/V — Capacitance
Capacitance equals charge stored divided by voltage across the capacitor.
Coulomb's Law — F = kq₁q₂/r²
The electrostatic force between two point charges is proportional to the product of the charges divided by the square of their separation.
E = kQ/r² — Electric Field of a Point Charge
Electric field equals Coulomb's constant times charge divided by distance squared.
V = kQ/r — Electric Potential of a Point Charge
Electric potential equals Coulomb's constant times charge divided by distance.
Electrical Power — P = IV
Electrical power equals current times voltage.
F = qvB·sinθ — Magnetic Force on a Moving Charge
Magnetic force equals charge times speed times field strength times the sine of the angle.
Ohm's Law — V = IR
Voltage equals current times resistance.
Calculators
Simulations
Practice
AC Circuits Practice
10 problems · 10 practice problems on AC circuits — RMS values, frequency, reactance and the AC/DC distinction.…
Capacitance Practice
10 problems · 10 practice problems on capacitance — capacitors, dielectrics, energy storage and RC timing.…
Circuits Practice — Ohm's Law, Series and Parallel
10 problems · 10 practice problems on electric circuits — Ohm's law, series and parallel resistors, and electric p…
Electric Field and Potential Practice
10 problems · 10 practice problems on electric fields and potential — field lines, E = F/q, and voltage as energy …
Electrostatics Practice
10 problems · 10 practice problems on electrostatics — charge, Coulomb's law, and charging by friction, conduction…
Electromagnetic Induction Practice
10 problems · 10 practice problems on electromagnetic induction — Faraday's law, Lenz's law, generators and transf…
Kirchhoff's Laws Practice
10 problems · 10 practice problems on Kirchhoff's laws — junction rule, loop rule, and multi-loop circuit analysis…
Magnetism Practice
10 problems · 10 practice problems on magnetism — magnetic forces, fields, compasses and the link between electric…