Electric Field Lines
Place charges in space and watch electric field lines form in real time. Understand superposition and field behavior visually.
Capacitors & Dielectrics
Build parallel plate capacitors, insert dielectrics, and observe how capacitance, charge, and energy storage change.
Photoelectric Effect
Animated photons knock electrons out of metals — Einstein's KE_max = hf − φ with 4 metal choices.
Threshold Frequency
KE_max vs f plot — zero below f₀ = φ/h, linear slope h above. Compare 4 metals.
KE vs Frequency
Parallel lines of slope h/e = 4.14 × 10⁻¹⁵ V·s — same slope, different intercepts per metal.
Intensity vs Current
Higher intensity → more photoelectrons → higher saturation current. Same V_s across intensities.
Stopping Potential
eV_s = hf − φ — split view: I–V curve + V_s vs f plot with live point.
Wave-Particle Duality
Double-slit with wave, particle, and both modes — see interference fringes build from discrete hits.
de Broglie Wavelength
λ = h/(mv) — Gaussian wavepacket across 4 particle types from electron to dust.
Electron Diffraction
Bragg diffraction 2d sinθ = nλ — Ni crystal lattice + I vs θ plot with n=1,2,3 peaks.
Matter Wave Visualization
Traveling Gaussian ψ(x,t) in position + |φ(k)|² in momentum — two reciprocal views.
Heisenberg Uncertainty
Δx · Δp ≥ ℏ/2 — tune position spread; momentum spread responds inversely. Live product.
Rutherford Model
Alpha scattering — toggle Thomson (pudding) vs Rutherford (point nucleus). Coulomb deflection.
Bohr Model
Circular orbits rₙ = n²a₀/Z with standing wave pattern nλ = 2πr.
Energy Levels
Eₙ = −13.6 Z²/n² eV — horizontal levels with continuum above the ionization limit.
Spectral Lines
Rydberg: 1/λ = R(1/n₁² − 1/n₂²) — selector for Lyman, Balmer, Paschen, Brackett, Pfund.
Hydrogen Spectrum
All 5 series on a log-wavelength axis with visible-band zoom toggle.
Transitions Between Levels
Click a level pair — photon animates out with wavelength-matched color.
Radioactive Decay
Stochastic decay of atoms vs theoretical N(t) = N₀e^(−λt) with λ = ln2/T½.
Half-Life
Stacked halving boxes — 4 isotopes (C-14, I-131, U-238, P-32).
Decay Curve
Side-by-side linear N(t) + semilog lnN(t) — slope = −λ on the log plot.
Binding Energy per Nucleon
Weizsäcker semi-empirical mass formula — peak at ⁵⁶Fe, labeled key nuclei.
Nuclear Reactions (Q-value)
Q = Δm · c² — preset D-T, D-D, p-Li fusion and U-235 fission reactions.
Nuclear Fission
Animated chain reaction — tune k to toggle subcritical / critical / supercritical.
Nuclear Fusion
D-T fusion overcoming Coulomb barrier — plasma T sets kinetic energy.
Mass–Energy Equivalence
E = mc² — mass in amu → J, MeV, kWh, megatons TNT. Presets for electron → ²³⁵U.
Energy Band Diagram
Valence and conduction bands split by E_g — tune T to see thermal excitation follow exp(−E_g/2kT).
Conductor vs Insulator vs Semiconductor
Three-panel side-by-side band comparison with resistivity labels.
Intrinsic Semiconductor
Pure Si lattice — thermal breaking of covalent bonds creates e⁻/hole pairs (n=p=n_i).
Extrinsic (n-type & p-type)
Doping with pentavalent P (extra e⁻) or trivalent B (extra hole) — toggle type live.
PN Junction
Depletion region, built-in V_bi = 0.7 V — apply forward/reverse bias and see width change.
Diode I-V Characteristics
Shockley: I = I_s(exp(V/V_T)−1) — knee at ~0.7 V Si; tiny reverse current.
Half-Wave Rectifier
Single diode — V_out = max(0, V_in − 0.7) with live oscilloscope trace.
Full-Wave Rectifier
Bridge of 4 diodes — V_out = |V_in| − 1.4 V with optional capacitor filter.
Transistor (NPN, CE)
I_C = β · I_B — tune V_BB through cutoff, active, and saturation regions.
Logic Gates
AND, OR, NOT, NAND, NOR, XOR — toggle A/B and watch output LED + truth table.
Zener Diode (Regulator)
Sharp reverse breakdown at V_z = 5.1 V — output clamps once V_in exceeds V_z.
LED Behavior
λ = 1240/E_g — 5 materials from GaAs (IR) to InGaN (violet) with photon emission.
Coulomb's Law
Drag two charges and watch the inverse-square force update live, with proper LaTeX formula.
Superposition of Forces
Drag a test charge among 4 fixed charges — net force = vector sum of individual forces.
Field Lines — Single Charge
Radial outward (+) or inward (−) lines with animated dots showing field direction.
Field Lines — Dipole
Streamlines from + to −. Adjustable separation. Animated dots travel along lines.
Field Lines — Multiple Charges
Two +, two −, quadrupole, three + — switch and watch the line patterns morph.
E vs r Curve
1/r² curve with live cursor. Check E falls fourfold when r doubles.
Field on Axis of Ring
E(z) = kQz/(z²+R²)^(3/2). Maximum at z=R/√2, demonstrated visually.
Infinite Line Charge
Radial E field perpendicular to a long charged wire. Falls as 1/r.
Infinite Plane Sheet
Uniform E = σ/2ε₀ — independent of distance from sheet.
Dipole — Axial vs Equatorial
Axial E is double the equatorial E at the same r (for a short dipole).
Torque on Dipole
τ = pE sinθ. Drag dipole to rotate, watch torque arrow flip.
Dipole SHM in Uniform Field
Oscillates with ω = √(pE/I). Includes damping for visual realism.
Electric Flux Through Surface
Φ = E·A·cosθ. Tilt the loop and watch flux follow a cosine curve.
Gauss's Law
Drag a charge in/out of a Gaussian sphere. Φ = Q_enc/ε₀ regardless of position inside.
Gaussian Surface — Sphere
E = 0 inside a uniformly charged shell, kQ/r² outside. Plot with live cursor.
Gaussian Surface — Cylinder
Closed Gaussian cylinder around a line charge. E = λ/(2πε₀r).
Field Inside a Conductor
Electrons drift to surface; E inside drops to zero in equilibrium.
Faraday Cage Shielding
Toggle the cage on/off — see how a closed conductor shields its interior.
E vs Conductor Shape
σ ∝ 1/R_curvature — sharp regions concentrate charge and produce strongest fields.
Charge on Connected Spheres
Same potential ⇒ Q ∝ R, σ ∝ 1/R. Smaller sphere has higher field.
Potential due to Point Charge
V = kq/r. Drag a probe and read live potential with full heatmap.
V & E vs Distance
1/r and 1/r² overlaid — confirm E = −dV/dr.
Equipotential Surfaces
Banded contours for single charge, dipole, two-+. Always perpendicular to E.
E = −dV/dx
Linear V → constant E. Graphs side-by-side.
Potential of Dipole
V = (kp cosθ)/r². Zero on equatorial plane, max on axis.
Work Moving a Charge
W = q(V_B − V_A). Independent of path between two equipotentials.
Parallel-Plate Capacitor
C = ε₀A/d. Animated dots show field. Live Q, E, U.
Effect of Dielectric
C' = κC₀. Toggle V-fixed (Q grows) vs Q-fixed (V drops).
Energy Stored in Capacitor
U = ½CV². Visualized as triangular area under Q-V curve.
RC Charging
q(t) = CV(1 − e^(−t/τ)). Watch the curve build with τ marked.
RC Discharging
q(t) = Q₀ e^(−t/τ). 37% remaining at τ marked clearly.
Capacitors in Series
1/C_eq = Σ 1/Cᵢ. Same Q. Voltage divides inversely with C.
Capacitors in Parallel
C_eq = ΣCᵢ. Same V. Charge splits proportionally to C.
Variable (Air-Gang) Capacitor
C ∝ |cosθ|. Rotate the shaft to tune from radio receiver-style sweep.
Dielectric Slab Insertion
Slab gets pulled in by force F = ε₀bV²(κ−1)/(2d).
Force Between Plates
F = Q²/(2ε₀A). Always attractive (opposite sign plates).
Dielectric Breakdown
Each dielectric has a breakdown E_max. Above it, the dielectric arcs.
Battery Removal Case
Insert dielectric with battery on/off — different physics. Compare side-by-side.
Ohm's Law (Animated)
V = IR with animated electron flow whose density scales with I.
V–I Characteristics
Compare ohmic (linear), diode (exponential), bulb (super-linear) curves.
R = ρL/A
Wire stretches/thins live; resistance updates accordingly.
R(T) — Materials Compared
Cu, Fe, W (positive α) vs Si (negative α). Linear plot.
Series Circuit
R_t = ΣRᵢ. Same I. V splits in proportion to each R.
Parallel Circuit
1/R_t = Σ1/Rᵢ. Same V. I splits inversely with R.
Wheatstone Bridge
Balance condition P/Q = R/S. Galvanometer reads zero when balanced.
Meter Bridge
Slide jockey along 1m wire; X = R·ℓ/(100−ℓ) at balance.
Kirchhoff's Laws
2-loop circuit solved live. Currents update with KCL+KVL system.
Loop Current Method
Two opposing EMFs around a loop — i = (ε₁−ε₂)/(R₁+R₂).
Internal Resistance & V_terminal
V = ε − Ir. As R drops, more voltage is wasted across r.
V–I Curve of Real Cell
y-intercept = ε, slope = −r. Short circuit at V=0.
Potentiometer
ε = kℓ. Slide jockey to find balance length on long wire.
Joule's Heating Law
H = I²Rt. Wire glows brighter at higher P. Live ΔT estimate.
Power — 3 Forms
P = VI = I²R = V²/R. Three bars stay equal as you change V, R.
Combination Circuit
R₁ in series with R₂||R₃. Live currents in each branch.
Drift Velocity
v_d = I/(nAe). Animated electrons with thermal motion + tiny drift.
Microscopic Current (Drude)
σ = ne²τ/m. See ions + electrons + collisions on atomic scale.
Battery Combinations
Series multiplies ε, parallel divides r. Toggle and watch I update.
Short Circuit
R_load → 0. I = ε/r. Wire overheats — visualized with red glow.
Bar Magnet & Dipole Field
Magnetic moment m = pole-strength × 2ℓ; field lines emerge from N, end at S.
Axial vs Equatorial Field
B_axial = (μ₀/4π)(2m/r³), B_equa = (μ₀/4π)(m/r³). Ratio = 2.
Earth's Magnetic Field
Declination, dip angle I, horizontal component H. tan I = 2 tan λ.
Magnetization & H, B Relation
M = χH, B = μ₀(H + M), μ_r = 1 + χ. Tune both to see effect.
Dia / Para / Ferromagnetic
Dipole alignment under H — dia opposite, para weak parallel, ferro strong.
B-H Hysteresis Loop
Soft iron (thin loop, low loss) vs hard steel (fat loop). Coercivity, retentivity.
Magnetic Flux
Φ = B·A·cosθ. Tilt the loop and watch flux follow a cosine curve.
Faraday's Law
ε = −N·dΦ/dt. Move a magnet near a coil and watch the galvanometer needle.
Lenz's Law
Induced current opposes the change in flux — repels approaching magnet, attracts retreating.
Motional EMF
ε = BLv. Rod sliding on rails through B field generates current and feels back-force.
Induced Electric Field
Changing B induces E circulating around it. E ∝ r inside, ∝ 1/r outside.
Self-Inductance & RL Transient
L = μ₀N²A/ℓ. RL circuit current I(t) = I∞(1 − e^(−t/τ)), τ = L/R.
Mutual Inductance
Two coupled coils. M = μ₀N₁N₂A/ℓ. ε₂ = −M·dI₁/dt with 90° phase shift.
Eddy Currents (Magnetic Braking)
Solid plate damps quickly in B; slotted plate barely damps. Lenz dissipation.
AC Source & Phasor
v(t) = V₀ sin(ωt). Rotating phasor projects onto sine wave. V_rms = V₀/√2.
AC through Resistor
I in phase with V (φ = 0°). I₀ = V₀/R.
AC through Inductor
I lags V by 90°. X_L = ωL grows with frequency.
AC through Capacitor
I leads V by 90°. X_C = 1/(ωC) falls with frequency.
Series LCR Circuit
Z = √(R² + (X_L − X_C)²). Phasor + impedance triangle live.
LCR Resonance
I peaks at f₀ = 1/(2π√LC). Q-factor and bandwidth Δf = f₀/Q.
Power & Power Factor
P_avg = V_rms·I_rms·cosφ. Watch p(t) = v·i and the average line.
LC Oscillations
q(t) = q₀cos(ω₀t). Energy bounces between capacitor and inductor.
Transformer
V_s/V_p = N_s/N_p. Step-up vs step-down with animated flux in core.
AC Generator
ε(t) = NBAω sin(ωt). Rotating coil between magnetic poles.
Reactance vs Frequency
X_L (linear ↑) and X_C (1/f ↓) crossing at resonance frequency f₀.
RMS Values
V_rms = V₀/√2 — DC equivalent for power. Mains 230 V is RMS, peak 325 V.
Phasor Addition (V_R, V_L, V_C)
Vector sum: V = √(V_R² + (V_L − V_C)²). Tune each and see V_net.
Displacement Current
I_d = ε₀·dΦ_E/dt. Maxwell's missing piece for the Ampère-Maxwell law.
EM Wave Propagation
E ⟂ B ⟂ direction. Sinusoidal transverse waves traveling at c = 3×10⁸ m/s.
EM Spectrum
From radio (km) → gamma (pm). Visible band 380–750 nm. Toggle bands.
Poynting Vector
S = (1/μ₀) E×B. Energy flow direction & intensity of EM wave.
Radiation Pressure
P = I/c (absorbed) or 2I/c (reflected). Light pushes objects.
λ × f = c
Tune wavelength and watch frequency adjust. Cross-spectrum interactive map.
Huygens' Principle
Each wavefront point emits secondary wavelets — envelope = new wavefront.
Young's Double-Slit
Fringe width β = λD/d. Live colored interference pattern on screen.
Single-Slit Diffraction
I = I₀(sin α/α)². First minimum at a sinθ = λ. Central max width 2λ/a.
Coherent Sources
Two synchronized sources — interference field with hyperbolic bright fringes.
Malus' Law (Polarization)
I = I₀cos²θ. Two polarizers — angle determines transmitted intensity.
Brewster's Angle
tan θ_B = n₂/n₁. Reflected ray fully polarized perpendicular to plane.
Diffraction Grating
N slits — sharper, brighter principal maxima at d sinθ = mλ.
Resolving Power (Rayleigh)
θ_min = 1.22 λ/D. Two Airy patterns transition resolved → unresolved.
Thin Film Interference
2nt cosθ_t = mλ — soap film, oil slick, anti-reflection coatings.