Physics

⚛️ Physics

Brownian Motion Simulation - 布朗运动模拟

Interactive simulation of Brownian motion demonstrating random particle movement and Einstein's diffusion theory. Features the fundamental equations: Mean Square Displacement <x²> = 2Dt, Einstein Relation: D = k_BT/(6πηr), Stokes' Law: F = 6πηrv, and Random Step: dx = √(2Ddt)·ξ where ξ~N(0,1). Real-time visualization includes: (1) Main canvas showing large particle's random trajectory with color-graded trail (blue→red indicating time progression), background small particles simulating thermal molecular motion, coordinate axes with origin marker, and displacement vector showing distance from starting point; (2) Distribution histogram displaying final displacement statistics from 100-trial runs comparing experimental data against theoretical Rayleigh distribution; (3) Real-time statistics: elapsed time, current displacement, mean square displacement (MSD), and diffusion coefficient D. Adjustable parameters: temperature T (100-500 K), particle radius r (0.1-5 μm), fluid viscosity η (0.1-10 mPa·s), time step dt (0.001-0.1 s), trail length (10-500 steps), and background particle count (0-200). Control modes: Start/Pause for single simulation, Reset to return to origin, and 'Run 100 Trials' for statistical analysis generating displacement distribution histogram. Display options: show/hide particle trail, background particles, coordinate grid, and color gradient trail. Educational content covers historical discovery by Robert Brown (1827), Einstein's 1905 theoretical explanation proving atomic existence, diffusion coefficient calculation using Boltzmann constant (k_B = 1.38×10⁻²³ J/K), Stokes' drag force balancing thermal fluctuations, and applications in statistical mechanics, polymer science, finance (stock models), biology (cell membranes), and nanotechnology. The simulation accurately demonstrates how higher temperature, smaller particles, or lower viscosity increase diffusion rate, and validates the theoretical relationship MSD = 2Dt over time. Multi-language support (zh, en, fr, de, es, ru, pt).

⚛️ Physics

Lenz's Law Demonstration - 楞次定律演示

Interactive demonstration of Lenz's law and electromagnetic induction with a coil, movable bar magnet, and galvanometer. Features Faraday's law: ε = -N·dΦ/dt, magnetic flux: Φ = ∫B·dA = B·A·cos(θ), Ohm's law: I = ε/R, and Lenz's law: induced current opposes magnetic flux change. Real-time visualization includes: (1) Main canvas showing copper wire solenoid coil with adjustable turns N, movable bar magnet with north/south poles, magnetic field lines emanating from magnet, flux vectors showing direction and magnitude through coil, and current direction indicators (⊙ for out, ⊗ for in); (2) Galvanometer display with needle deflection showing current direction and magnitude, scale from -I to +I with zero center, and real-time current direction label; (3) Three real-time charts: Magnetic Flux vs Time (Φ), Induced EMF vs Time (ε), and Induced Current vs Time (I). Adjustable parameters: magnet speed (1-20 cm/s), coil turns N (10-500), resistance R (1-100 Ω), coil radius r (2-10 cm), magnet strength B₀ (10-100 mT), and animation speed (0.1-3.0x). Animation modes: Insert (magnet moves into coil), Extract (magnet moves out of coil), and Auto (continuous oscillation). Display options: show/hide magnetic field lines, current direction indicators, flux vectors, and coil details. Educational content covers magnetic flux concept, Faraday's induction law derivation, Lenz's law explanation with energy conservation, and practical applications: transformers, electric generators, induction motors, electromagnetic braking systems, metal detectors, and wireless charging. The visualization clearly demonstrates that inserting a magnet (increasing flux) induces current that creates opposing field, while extracting (decreasing flux) reverses current direction. Multi-language support (zh, en, es, fr, de, ru, pt).

⚛️ Physics

Free Fall Motion - 自由落体运动

Interactive visualization of free fall motion under gravity with ball physics and energy conservation. Features kinematic equations: h(t) = h₀ - ½gt² + v₀t for height, v(t) = v₀ - gt for velocity, where g ≈ 9.8 m/s². Real-time visualization includes: (1) Main animation canvas showing ball falling vertically under gravity with motion trail and velocity indicator arrow, adjustable ground level and scaling; (2) Real-time data display panel showing current height (h), velocity (v), elapsed time (t), and gravitational acceleration (g); (3) Height vs Time chart displaying parabolic trajectory h(t) with current position marker; (4) Velocity vs Time chart showing linear relationship v(t) with current velocity indicator; (5) Energy conservation bars with three components: Potential Energy (mgh) shown as orange-yellow gradient bar, Kinetic Energy (½mv²) shown as green-blue gradient bar, and Total Energy (PE + KE) shown as purple-pink gradient bar, demonstrating energy conservation principle; (6) Interactive parameter controls: Initial height h₀ (10-200 m), Initial velocity v₀ (-50 to +50 m/s), and Mass m (0.1-10 kg); (7) Visualization options: Show Trail (position history), Show Grid (height scale lines), and Show Energy Bars; (8) Quick presets: Simple Drop (h₀=100m, v₀=0), Throw Up (h₀=50m, v₀=+20m/s), High Throw (h₀=80m, v₀=+30m/s, m=2kg), and Heavy Object (h₀=100m, v₀=+10m/s, m=5kg); (9) Animation controls: Start, Pause, and Reset buttons for motion control. Educational content covers gravitational acceleration, kinematic equations, energy transformations (potential to kinetic), conservation of mechanical energy, projectile motion principles, and real-world applications: skydiving (parachute deployment, terminal velocity), sports (basketball shots, javelin throws, diving), engineering (elevator design, amusement park rides), and space science (orbital mechanics). Physics formulas section includes: Height equation h(t) = h₀ - ½gt² + v₀t, Velocity equation v(t) = v₀ - gt, Potential Energy PE = mgh, Kinetic Energy KE = ½mv², and Total Energy E = PE + KE = constant. Multi-language support (en, fr, de, es, pt, ru, zh).

⚛️ Physics

Series and Parallel Circuits - 串联/并联电路

Interactive visualization of series and parallel circuits with two resistors, featuring dual-mode switching between series and parallel configurations. Real-time visualization includes: (1) Circuit diagram showing series circuit (resistors R₁ and R₂ connected end-to-end) or parallel circuit (resistors R₁ and R₂ connected across same two points), with voltage source, current flow arrows, animated current flow, and real-time parameter displays; (2) Component data panel showing individual resistor data: voltage across each resistor (V₁, V₂), current through each resistor (I₁, I₂), and power dissipated by each resistor (P₁, P₂); (3) Current distribution chart with color-coded bars comparing I₁ (R₁) and I₂ (R₂); (4) Power distribution chart displaying P₁ (R₁) and P₂ (R₂) consumption; (5) Applicable formulas panel updating based on circuit mode (series or parallel). Key formulas: Series - R_total = R₁ + R₂, I_total = V/R_total, I₁ = I₂ = I_total, V₁ = I×R₁, V₂ = I×R₂, P = I²R; Parallel - 1/R_total = 1/R₁ + 1/R₂ or R_total = (R₁×R₂)/(R₁+R₂), V₁ = V₂ = V_source, I₁ = V/R₁, I₂ = V/R₂, I_total = I₁ + I₂, P = V²/R. Adjustable parameters: voltage source V (1-24 V), resistor R₁ (1-100 Ω), and resistor R₂ (1-100 Ω). Quick presets: Equal Resistors, High R₁, High R₂, Low Voltage, and High Voltage. Visualization options: show/hide current flow animation, values on circuit, and current flow animation. Animation controls: Start, Pause, and Reset. Educational content covers series circuits (same current, voltage division), parallel circuits (same voltage, current division), key differences between configurations, real-world applications (household wiring, string lights, battery configurations, automotive systems), and problem-solving strategies. Comparison highlights: Series has same current throughout and divides voltage; parallel has same voltage across components and divides current. Series increases total resistance; parallel decreases total resistance. Parallel circuits are more reliable as one component failure doesn't affect others. Multi-language support (en, fr, de, es, pt, ru, zh).

⚛️ Physics

Kirchhoff's Circuit Laws - 基尔霍夫电路定律

Interactive visualization of Kirchhoff's circuit laws (KCL and KVL) with real-time circuit analysis and calculation. Features Kirchhoff's Current Law (KCL): ΣI_in = ΣI_out, Kirchhoff's Voltage Law (KVL): ΣV = 0, and Ohm's Law: V = IR. Real-time visualization includes: (1) Interactive circuit diagram with 2-3 nodes (A, B, C), series resistor R₁ and parallel resistors R₂, R₃, current flow arrows (I₁, I₂, I₃), voltage source, and real-time parameter displays; (2) Current distribution chart showing I₁ (total current), I₂ (branch 1), and I₃ (branch 2) with color-coded bars; (3) Power distribution chart displaying P₁ (R₁), P₂ (R₂), and P₃ (R₃) consumption; (4) Voltage drops section showing individual voltage drops across each resistor; (5) Law verification panel with KCL equation (I₁ = I₂ + I₃) and KVL equations for both loops with real-time calculation and error checking. Adjustable parameters: voltage source V (1-24 V), series resistor R₁ (1-50 Ω), parallel resistor R₂ (1-50 Ω), and parallel resistor R₃ (1-50 Ω). Quick presets: Balanced Circuit (R₂ = R₃), High R₁, High R₂, Low Voltage, and Custom Parameters. Visualization options: show/hide current flow animation, voltage drops, power values, and current animation. Animation controls: Start, Pause, and Reset for current flow animation. Real-time calculations: total current I₁ = V/(R₁ + R₂||R₃), branch currents using current divider rule, voltage drops across each resistor, and power consumption P = VI = I²R. Educational content covers KCL (current conservation at nodes), KVL (voltage conservation around loops), Ohm's law applications, parallel resistance calculation (1/R_parallel = 1/R₂ + 1/R₃), power calculation methods, and problem-solving strategies for circuit analysis. Historical context covers Gustav Kirchhoff (1824-1887) and the development of circuit analysis fundamentals. Multi-language support (zh, en, fr, de, es, pt, ru).

⚛️ Physics

Capacitor Charge/Discharge - 电容充放电

Interactive RC circuit simulation demonstrating capacitor charging and discharging with exponential voltage/current curves, time constant visualization, and circuit animation. Features charging equation: q(t) = Q₀(1 - e^(-t/RC)), discharging equation: q(t) = Q₀·e^(-t/RC), time constant: τ = RC, voltage: V = q/C, charging current: I = (V₀/R)·e^(-t/RC), discharging current: I = -(Q₀/RC)·e^(-t/RC). Real-time visualization includes: (1) Circuit diagram with animated switch connecting battery (charge) or short circuit (discharge), resistor, and capacitor; (2) Electron flow animation showing current direction and magnitude; (3) Charge accumulation animation with positive (red) and negative (blue) charges on capacitor plates; (4) Real-time voltage meter displaying capacitor voltage; (5) Charge/discharge curves showing q(t) exponential behavior with theoretical curves overlay; (6) Split-screen comparison view showing charging vs discharging side by side; (7) Current curve I(t) showing positive (charge) and negative (discharge) exponential decay. Adjustable parameters: resistance R (10-1000 kΩ), capacitance C (1-100 μF), source voltage V₀ (1-50 V), animation speed (0.1-3.0x), time window (5-30 s), particle animation speed (0.5-2.0x), and curve opacity (0.3-1.0). Display options: show/hide electron flow, charge accumulation, voltage meter. Time constant markers show τ, 2τ, 3τ, 4τ, 5τ positions on curves (63.2%, 86.5%, 95.0%, 98.2%, 99.3% charged/discharged). Educational content covers exponential charging/discharging process, RC time constant significance, energy storage: E = ½CV² = q²/(2C), practical applications: timing circuits, filters, power supply smoothing, camera flash units, defibrillators, energy storage in regenerative braking, touchscreens, coupling/decoupling in amplifiers, and memory elements. Multi-language support (zh, en, de, fr, es, ru, pt).

⚛️ Physics

Plane Mirror Imaging - 平面镜成像

Interactive visualization of plane mirror imaging demonstrating virtual image formation with ray tracing. Features mirror imaging formulas: image distance d_i = -d_o (negative for virtual image), magnification m = h_i/h_o = +1 (upright, same size), law of reflection θ_i = θ_r (incident angle = reflected angle). Real-time visualization includes: (1) Object (solid red arrow) with adjustable position and height; (2) Virtual image (dashed blue arrow) behind mirror at equal distance; (3) Mirror with hatched back indicating reflective surface; (4) Light ray tracing: incident rays (orange) from object to mirror, reflected rays to observer, virtual ray extensions (blue dashed) showing apparent origin from virtual image; (5) Observer eye position with field of view visualization; (6) Normal line perpendicular to mirror surface. Interactive controls: object distance (20-200 px), object height (20-150 px), object tilt angle (-30° to 30°), eye position (50-300 px), eye height (-100 to 150 px), mirror height (100-400 px), mirror tilt angle (-30° to 30°). Toggle options: show/hide light rays, virtual ray extensions, observer eye, field of view. Three preset configurations: vertical mirror, tilted mirror, full-length mirror. Real-time info display: object distance (m), image distance (m), magnification (1.0x), image type (Virtual). Educational content covers: what is plane mirror imaging (based on law of reflection, virtual upright same-size image), virtual image formation (rays appear to diverge from point behind mirror, cannot be projected on screen), symmetry principle (object and image equidistant from mirror, lateral inversion left-right reversal, up-down NOT inverted), ray tracing rules (perpendicular ray reflects back, arbitrary ray reflects with equal angles, backward extensions intersect at image), field of view (depends on mirror size, observer distance, object position; mirror needs at least half object height for full reflection), practical applications (dressing mirrors, periscopes, kaleidoscopes, optical instruments, rearview mirrors, solar mirrors), and lateral inversion (left-right swap, coordinate system reversal, why text appears reversed, ambulance signs). Multi-language support (zh, en, es, fr, de, ru, pt).

⚛️ Physics

Charge Interaction - 两种电荷相互作用

Interactive visualization of charge interaction demonstrating Coulomb's law with four scene switching: positive-positive (repulsion), negative-negative (repulsion), positive-negative (attraction), negative-positive (attraction). Features Coulomb's law formula: F = k·q₁·q₂/r². Real-time visualization includes: (1) Two charges with adjustable signs (+/-) and magnitudes; (2) Force vectors showing interaction direction (red arrows for repulsion, green arrows for attraction); (3) Motion animation with physics-based movement; (4) Electric field lines distribution; (5) Potential energy markers (U = k·q₁·q₂/r, positive for repulsion, negative for attraction). Four scene buttons: ++ (repel), -- (repel), +- (attract), -+ (attract). Animation controls: enable/disable motion, adjust speed, toggle field lines, force vectors, and potential markers. Parameter adjustments: charge magnitude (1-10), initial distance (100-400 px). Reset button to restart animation from initial positions. Educational content covers Coulomb's law statement and mathematical formulation, attraction vs repulsion principle (like charges repel, opposite charges attract, 同种相斥，异种相吸), force direction (along the line connecting charges, 沿连线方向), electric potential energy (positive for repulsion systems, negative for attraction, potential energy decreases as system moves toward equilibrium), and field line visualization (field lines from positive charges to negative charges, never cross, perpendicular to equipotential surfaces). Practical applications: atomic structure (electron-nucleus attraction, electron-electron repulsion), electrostatic precipitators, photocopiers and laser printers (charged toner attraction), particle accelerators, biological systems (nerve impulses from ion movement), and everyday phenomena (static electricity, lightning). Multi-language support (zh, en, es, fr, de, ru, pt).

⚛️ Physics

RLC Circuit Oscillation - RLC电路振荡

Interactive RLC circuit simulation demonstrating damped harmonic oscillations, resonance phenomena, and energy transfer between electric and magnetic fields. Features differential equation: Lq"" + Rq" + q/C = 0, natural frequency ω₀ = 1/√(LC), damping coefficient γ = R/(2L), damping ratio ζ = γ/ω₀, damped frequency ωd = √(ω₀² - γ²). Real-time visualization includes: (1) Waveform view showing charge Q(t) and current I(t) with exponential decay envelope; (2) Phase portrait (Q vs I) displaying spiral trajectory toward origin for damped systems; (3) Frequency response curve showing resonance peak at ω₀ with quality factor Q = ω₀L/R; (4) Energy transfer view showing continuous conversion between electric field energy (UE = q²/2C), magnetic field energy (UB = LI²/2), and heat dissipation (P = I²R); (5) Circuit diagram with R, L, C components and current flow. Adjustable parameters: resistance R (0-100 Ω), inductance L (0.1-10 H), capacitance C (0.1-5.0 F), initial charge Q₀ (1-20 C), animation speed (0.1-3.0x), time window (10-60 s), phase trail length (1-10), envelope scale (0.5-2.0x). Toggle display of charge and current curves independently. Five damping modes: underdamped (ζ < 1) with oscillatory decay, critically damped (ζ = 1) with fastest non-oscillatory return, overdamped (ζ > 1) with slow exponential decay. Educational content covers second-order differential equations, characteristic equation roots, relationship between circuit parameters and damping behavior, resonance condition and Q factor, energy conservation and dissipation, phase space analysis, and practical applications: tuning circuits (radio, TV), filters (audio, signal processing), oscillators and clock generators, voltage regulators, impedance matching, induction heating, wireless power transfer, and damping systems. Color coding: blue/cyan for charge Q, red for current I, green for energy, orange for dissipated heat. Multi-language support (zh, en, de, fr, es, ru, pt).

⚛️ Physics

Three Elements of Sound - 声音的三要素

Interactive visualization of the three elements of sound: pitch (音调), loudness (响度), and timbre (音色). Features pitch control via fundamental frequency f₀ (100-1000 Hz) showing wave density changes, loudness control via amplitude A with sound level calculation L = 20log₁₀(A/A₀) dB, and timbre switching between sine wave (纯音), square wave (方波), sawtooth wave (锯齿波), and piano sound (钢琴声) with different harmonic structures. Real-time dual-canvas visualization: (1) Time-domain waveform display showing actual audio from Web Audio API or theoretical waveform based on parameters; (2) Frequency-domain spectrum display using FFT analysis showing harmonic components and frequency distribution. Web Audio API integration: real-time sound generation and playback with oscillator nodes for basic waveforms and multi-oscillator piano simulation with 8 harmonics (1, 0.5, 0.3, 0.2, 0.1, 0.05, 0.03, 0.02). Visual feedback: pitch → waveform density (高频密集/低频稀疏), loudness → waveform amplitude (振幅大时波形高), timbre → waveform shape and harmonic distribution. Preset controls: frequency presets (low 220 Hz, mid 440 Hz, high 880 Hz), amplitude presets (soft 0.2, medium 0.5, loud 0.8), and musical note display (e.g., A4 for 440 Hz). Educational content covers fundamental frequency and pitch perception (音调由基频决定), amplitude and sound level in decibels (响度由振幅决定, L = 20log₁₀(A/A₀) dB), timbre and harmonic composition (音色由谐波组成决定), time-domain vs frequency-domain analysis (时域波形与频域频谱的傅里叶变换关系), and practical applications: music production and audio engineering (EQ调整音色), speech recognition (语音识别中的音调和音色特征提取), acoustic design (音乐厅和录音棚声学设计), hearing aids and cochlear implants (助听器频率和响度调节), music therapy (音乐治疗中的心理效应), sound synthesizers (声音合成器创造各种音色), telecommunication bandwidth compression, and noise control analysis. Multi-language support (zh, en, es, fr, de, ru, pt).

⚛️ Physics

Electromagnetic Wave Propagation - 电磁波传播

Interactive electromagnetic wave visualization demonstrating perpendicular E and B fields, wave propagation, Poynting vector, and Maxwell's equations. Features EM wave formulas: E = E₀sin(kx - ωt) ŷ, B = B₀sin(kx - ωt) ẑ, wave speed c = 1/√(ε₀μ₀) = λf ≈ 3×10⁸ m/s, energy density u = ½ε₀E² + ½(B²/μ₀), Poynting vector S = E × H. Real-time 3D visualization includes: (1) Electric field (blue) oscillating in y-direction; (2) Magnetic field (red) oscillating in z-direction; (3) Wave propagation along x-axis with E ⟂ B ⟂ propagation direction; (4) Optional Poynting vector (green) showing energy flow; (5) Energy density view showing oscillating energy distribution. Adjustable parameters: frequency f (0.1-3.0 Hz), amplitude E₀,B₀ (0.1-2.0), wave number k (0.5-3.0), animation speed (0-3.0x), rotation angle (0-360°) for 3D perspective, vector density (10-40), envelope scale (0.5-2.0x). View modes: 3D perspective (both fields), E field only, B field only, and energy density. Display options: toggle E field, B field, Poynting vector, and propagation direction independently. Animation controls: play/pause, reset, and speed adjustment. Educational content covers Maxwell's equations predicting EM waves, field properties (in phase, perpendicular, transverse, E = cB), energy and momentum transport via Poynting vector, electromagnetic spectrum (radio to gamma rays), polarization (linear, circular), and practical applications: wireless communication (radio, TV, mobile, WiFi, satellite), medical imaging (X-ray, MRI, CT), optical technologies (lasers, fiber optics), remote sensing (radar, astronomy), industrial uses (microwave, UV curing), solar sails, optical tweezers, and quantum technologies. Color coding: blue for E field, red for B field, green for Poynting vector, purple for energy density. Multi-language support (zh, en, es, fr, de, ru, pt).

⚛️ Physics

Coulomb's Force vs Distance - 库伦力与距离

Interactive visualization of Coulomb's law showing force vs distance relationship. Features Coulomb's law formula: F = k·q₁·q₂/r², where k = 8.99×10⁹ N·m²/C². Real-time dual-canvas visualization: (1) Force visualization canvas showing two charges q₁ and q₂ with adjustable distance r, force vectors showing attraction (green arrows pointing toward each other) or repulsion (red arrows pointing away), color-coded charges (red for positive, blue for negative) with glow effects; (2) Force vs distance graph canvas plotting F-r curve with current position marker, logarithmic scale option to visualize inverse square law. Adjustable parameters: charge q₁ (-10 to +10 μC), charge q₂ (-10 to +10 μC), distance r (0.1 to 2.0 m), vector scale (0.1-3.0x). Display options: toggle force vectors, grid overlay, and logarithmic scale. Quick preset buttons for all four charge combinations: positive-positive (repulsion), negative-negative (repulsion), positive-negative (attraction), negative-positive (attraction). Educational content covers Coulomb's law statement and mathematical formulation, inverse square relationship (F ∝ 1/r²), attraction vs repulsion (like charges repel, opposite charges attract), comparison with Newton's law of universal gravitation (both inverse square laws, but electric forces much stronger ~10³⁶×), force calculation with unit conversion (μC to C), and practical applications: atomic structure and electron configurations, ionic and covalent chemical bonding, electrostatic precipitators, mass spectrometry, capacitor design, plasma physics and fusion reactors, static electricity and lightning. Real-time force value display with automatic unit scaling (N, mN, μN). Multi-language support (zh, en, es, fr, de, ru, pt).