電楽

DENRAKU is a simulation app that visualizes the "invisible phenomena" of electromagnetism in real time. Experience the world of electricity and magnetism through beautiful visuals and intuitive touch controls.

This is the electromagnetism edition of the physics simulation series "BUTURAKU." It allows you to understand the concepts of electromagnetism learned in middle school, high school, and university science classes not only through mathematical formulas but also through moving images.

10 types of simulations:

- Electric Field: Tap to place positive charges (+), long press to place negative charges (-). Electric field lines and a field intensity color map are drawn according to Coulomb's law, and light particles flow along the field lines. Charges can be moved by dragging.

- Circuit: A series circuit is simulated using Ohm's law (V=IR). Observe changes in current using voltage and resistance sliders. Current particles flow across the circuit diagram, and battery and resistor symbols are realistically drawn.


- Electromagnetic Induction: Visualizes Faraday's law (EMF = -NdΦ/dt). Dragging the magnet closer to or further away from the coil changes the EMF meter and current graph in real time.

- Capacitor: Displays the charging and discharging of an RC circuit using an exponential curve animation. Three synchronized graphs for charge Q(t), current I(t), and voltage V(t) visually illustrate the meaning of the time constant τ. Tap to switch between charging and discharging.

- Magnetic Field: Tap to place a bar magnet. Magnetic field lines flow from the north pole to the south pole according to the magnetic dipole model (B ∝ 1/r³), and the magnetic field is visualized with a magnetic field strength heatmap and cyan light particles. Long press to delete, drag to move.

- Electromagnetic Wave: Displays an animation of electromagnetic waves propagating with the electric field E (red) and magnetic field B (blue) orthogonal to each other. Freely adjust the wavelength, amplitude, and frequency using the sliders. Includes explanations of Maxwell's equations, c = λf, and Poynting vectors.

- Transformer: Simulates the mutual induction of primary and secondary coils coupled by an iron core. Observe how the voltage ratio V₂/V₁ = N₂/N₁ and the current ratio I₂/I₁ = N₁/N₂ interact by changing the primary voltage, frequency, primary/secondary turns ratio, and load resistance. Includes explanations of power conservation and induced electromotive force.

- Hall Effect: When a magnetic field is applied to a conductor carrying current, the carriers are biased by the Lorentz force, generating a Hall voltage Vₕ in the lateral direction. Observe how the storage side changes with the switching of electrons and holes, and the sign reversal of the current and magnetic field. Learn the formula Vₕ = IB/(nqt), used in semiconductor evaluation, intuitively.


- Generator: Visualizes the sinusoidal electromotive force ε = NBAω sin(ωt) generated by a coil rotating in a magnetic field. By changing the magnetic field, coil turns, angular frequency, and load resistance, you can observe the relationship between the peak electromotive force ε₀ = NBAω and the output power P = ε²/R in the waveform.

- Ionic Conduction: Visualizes how cations and anions in an electrolyte solution drift in opposite directions due to an electric field. By changing the applied voltage, ion concentration, mobility, and temperature, you can experience the drift velocity vd = μE and electrical conductivity σ = nqμ.

Features:
- Real-time electromagnetic simulation (10 types)
- Intuitive touch operation (tap, long press, drag)
- Freely adjust parameters with sliders
- Physics explanation sheet included for each simulation
- Dark/light theme switching support
- Japanese and English support (automatically follows device language settings)
- No login required, ready to use immediately