Electricity & Magnetism
Electric fields, circuits, Ohm's law, and electromagnetic induction
Cherenkov Radiation Cone
Charged particle in a medium of refractive index n: spherical wavefronts of phase velocity c/n pile up on a Mach-like cone with half-angle cos θ_c = 1/(βn) once β > 1/n. Animated wavefronts, magenta cone envelope and material presets (water, glass, diamond) explain the blue glow of pool reactors and IceCube/Super-Kamiokande detection.
Bar Magnet & Iron Filings
Drag-and-drop bar magnet on a card of iron-filing rods; each filing aligns with the local two-pole B field.
Biot–Savart Law
Infinite wire B ∝ 1/r; ring via segment sum; heatmap + probe.
Electric Dipole Field (2D)
±q on axis: V heatmap, equipotentials, E field lines; formulas.
Ideal Op-Amp (feedback)
Inverting, non-inverting, buffer; sine or DC; optional rail clipping.
Van de Graaff Generator
Belt charges a dome; V = Q/C; stylized spark to ground when V_break is exceeded.
Kirchhoff's Laws (KCL & KVL)
3-node DC: junction divider + optional R∥V; hints, KCL/KVL, solved currents.
Plane EM Wave (vacuum)
E ⊥ B ⊥ k: sin(kz−ωt) fields, Poynting along z; ω = ck (c = 1).
DC Motor & Generator
Coil in B: motor V = IR + kω, generator E = kω into a load — same k, two modes.
Gradient-B Drift
B_z(x,y) with weak gradient; orbit from q(E+v×B) at local B — gyration + drift.
Magnetic Mirror (Bottle)
Axial B(z) pinch; μ adiabatic invariant, v∥ from −μ ∂B/∂z — Van Allen / mirror sketch.
Dipole Radiation Pattern
Time-averaged power ∝ sin² θ in the plane containing the dipole axis (far-field cartoon).
Half-Wave Dipole Antenna Pattern
Far-field E-plane pattern of a thin λ/2 wire: power ∝ [cos(½π cos θ)/sin θ]², directivity D ≈ 1.64 (~2.15 dBi); optional sin² θ overlay vs a short dipole.
Rotating Dipole E-field
±q orbit in the plane: Coulomb superposition arrows — near-field sketch before full radiation.
Bode Diagram (RC low-pass)
|H| in dB and phase vs log f; f_c = 1/(2πRC) marked — first-order pole intuition.
Nyquist Plot (linear systems)
Open-loop L(jω) in the complex plane vs frequency; critical point −1 and distance teaching aid.
DC–DC Buck / Boost
Ideal CCM averages: buck V_out ≈ D·V_in, boost V_out ≈ V_in/(1−D); schematic + ripple cartoon.
Buck Converter Ripple
Step-down DC-DC converter: duty cycle, inductor ripple, CCM/DCM boundary, capacitor ESR ripple, and switching waveform sketch.
Boost Converter
Step-up DC-DC converter: Vout = Vin/(1−D), inductor current ripple, MOSFET/diode states, CCM/DCM hint, and output ripple.
Solar Cell I–V & MPP
Single-diode cell: photocurrent vs irradiance, ideality n, temperature; I(V), power P(V), maximum-power point.
Battery Thevenin (SOC)
V_oc(SOC), R_int(SOC), Coulomb-counted SOC vs charge/discharge current; terminal voltage trace.
Skin Depth & Proximity Effect
δ = √(2/(ωμσ)), current crowding in round conductors, proximity effect, and estimated AC resistance vs frequency.
Debye Shielding in a Plasma
Test charge in an electron plasma: Yukawa potential φ ∝ e^{-r/λ_D}/r, λ_D = √(ε₀k_BT/n_e e²), 2D map and λ_D vs T, n.
Langmuir Plasma Oscillations
Collective electron oscillations at ω_p = √(n_e e²/ε₀m_e): animated δn wave, Bohm–Gross dispersion ω(k), and ω_p vs density.
Alfvén Wave on a Magnetic Field Line
Transverse MHD Alfvén wave: v_A = B/√(μ₀ρ), animated field-line displacement, standing modes and pulse reflections at fixed boundaries.
Magnetic Reconnection (Sweet–Parker)
Toy Sweet–Parker X-point: opposite B-regions, current sheet, inflow v_in ≈ v_A/√S and outflow, Lundquist number S and sheet thickness δ/L.
Parker Spiral Solar Wind
Rotating Sun plus radial solar wind: interplanetary B spirals with tan ψ = Ωr/v_sw, animated field lines (top view), ψ(r) and |B| falloff.
Radiation Belts Drift Shells
Van Allen belts: gradient and curvature drift on dipole L-shells, mirror latitude, equatorial loss cone α_lc(L); electrons west, protons east.
Eddy Current Tube
Magnet fall: dv/dt = g in air vs g − k v in copper pipe (toy drag model).
Plasma Ball (Stylized)
Glass sphere, center electrode, streamers toward cursor — visual only.
PN Junction & Diode
Band cartoon and Shockley-style I(V); ideality, temperature, I₀ scale.
TDR Transmission-Line Pulses
Voltage step into a cable: open/short/mismatch reflections, Γ, source re-reflections, time-of-flight, and distance from echo.
Phased Array
Uniform linear array factor vs steering phase and element spacing.
Yagi–Uda Antenna
Reflector, driven element, and directors: teaching pattern plus gain vs number of directors (schematic model).
Smith Chart & Matching
Click to set normalized Z; series L/C along constant-r arcs and shunt L/C via Y = 1/Z; Γ, SWR, matching trail.
VSWR & Standing Wave (Transmission Line)
Complex Z_L → Γ and VSWR; voltage magnitude envelope and animated Re{V} along a lossless line.
Rectangular Waveguide TE₁₀
Dominant mode fields (E_y, H_x, H_z), cutoff f_c = c/(2a√ε_r), β and guide wavelength λ_g.
Compton Scattering
Photon wavelength shift vs angle; λ_C ≈ 2.426 pm.
Electric Field Visualizer
Place charges and watch field lines update in real time.
Electric Potential
2D heatmap V = Σ kq/r. Drag charges, see equipotential colors.
Coulomb's Law
Two charges with adjustable magnitude and distance. Force vectors shown.
Parallel-Plate Capacitor
C = ε₀εᵣA/d, E = V/d, Q and energy; plates and C vs d.
Three-Phase AC Waveforms
Phase and line voltages, phasors, star/delta relation, line current, power factor, and P/Q/S power triangle.
Hall Effect
U_H = R_H I B / t; R_H sign for e⁻ vs holes; B, I, n, t.
Photoelectric Effect
E = hc/λ vs φ, K_max, V_s; I vs λ and vs intensity (model).
Particle in E and B Fields
Lorentz force: cyclotron motion, E×B drift, trajectories in sim units.
Circuit Builder
Drag and drop components: battery, resistor, bulb, switch. See current flow.
Ohm's Law
Adjust voltage and resistance. See current change with interactive V-I graph.
Series & Parallel
Compare total resistance and current distribution side by side.
RC Circuit
Charging and discharging capacitor with exponential curves.
RC Filter (LP / HP)
Bode gain vs frequency, f_c at −3 dB; live sine V_in and V_out.
RL Circuit
Series RL: τ = L/R, i(t) rise & decay, v_L; DC steady i = V/R.
RLC Series (AC)
Resonance peak, |Z|, phase. I(f) curve and live V & I waves.
Resistor Color Code
Click bands to see resistance, or enter value to see bands.
Magnetic Field
Bar magnets and current-carrying wires with field line visualization.
Electromagnetic Induction
Move magnet through coil. Faraday's law visualized.
Transformer Equivalent Circuit
Turns ratio with magnetizing branch, leakage reactance, copper/core losses, load regulation, and efficiency versus load.
Induction Motor Torque-Speed Curve
Slip, synchronous speed, breakdown torque, starting current, stable operating point, and V/f control sketch.
Mutual Inductance
Coupled L₁, L₂ with k and M; sinusoidal primary drives secondary current through R₂.
Mass Spectrometer (Sector)
Velocity selector v = E/B then magnetic sector: different m/q bend to different radii (2D schematic).
Resonant Transformer (Tesla-style)
Coupled RLC tanks; tune f_drive near secondary ω₀ to grow V on high‑Q side (linear coupled ODEs).
Wheatstone Bridge
Four arms, G between mid nodes; V_B − V_C and null when R₁R₄ = R₂R₃.
Dipole in Uniform E
τ = −pE sin θ, U = −pE cos θ; damped rotation; optional AC on E.
Ferrofluid (Stylized)
Purple metaball pool, spikes, field-line hints — visual only, not MHD.
Cyclotron (Schematic)
B uniform, oscillating E in gap; spiral growth; ω_c = (q/m)B in sim units.