DENRAKU - Electromagnetism Sim

DENRAKU is an interactive educational app that visualizes the invisible world of electromagnetism in real time. Touch and move fields, currents and waves to connect the equations with what you see.

Developer: Fuji Bit Inc.

DENRAKU is the electromagnetism edition of the "-raku" physics simulation series. It turns the electromagnetism of school and university physics into moving pictures, not just formulas.

12 simulations in 3 categories:

- Electricity and current
- Electric Field: Place positive (+) charges with a tap or negative (-) charges with a long press. Field lines and a strength map follow Coulomb's law, with particles flowing along the lines. Drag charges to reshape the field.
- Capacitor: Watch an RC circuit charge and discharge. Synced graphs of Q(t), I(t) and V(t) show what the time constant tau means.
- Circuit: Explore Ohm's law (V = IR) with a series circuit. Adjust voltage and resistance with sliders and watch current particles speed up or slow down.
- Ion Conduction: See cations and anions drift in opposite directions inside an electrolyte. Adjust voltage, ion density, mobility and temperature to explore drift velocity (vd = mu E) and conductivity (sigma = nq mu).

- Magnetism and induction
- Magnetic Field: Place bar magnets and observe dipole field lines (B proportional to 1/r^3) from the N pole to the S pole, with a field strength heatmap and cyan particles. Drag to move magnets, long press to remove them.
- Field of a current (new): See the field lines and compass needles around a straight wire, a circular loop and a solenoid, shown in cross-section. Drag the probe to read the magnetic flux density B in microtesla at any point. The loop and solenoid are computed from the exact 3D field of circular currents, so you can check the right-hand rule.
- Hall Effect: Apply a magnetic field to a current-carrying conductor and watch the Lorentz force deflect carriers, producing the Hall voltage Vh = IB/(nqt). Switch between electrons and holes to see the accumulation side reverse.
- Electromagnetic Induction: Drag a magnet toward and away from a coil. A real-time meter and graph show Faraday's law (EMF = -N dPhi/dt) and Lenz's law in action.

- AC and electromagnetic waves
- Generator: See how a coil rotating in a magnetic field generates a sinusoidal EMF, epsilon = NBA omega sin(omega t). Tune the field, turns, angular frequency and load to study the peak EMF and output power.
- Transformer: Simulate mutual induction between primary and secondary coils on an iron core. Adjust voltage, frequency, turns ratio and load to see V2/V1 = N2/N1 and I2/I1 = N1/N2 in real-time waveforms.
- RLC AC circuit (new): Apply an AC voltage to a series circuit of a resistor R, an inductor L and a capacitor C. Charges moving back and forth in the circuit, voltage and current waveforms, a phasor diagram and the resonance curve are shown together. Sweep the frequency to see the phase shift and resonance, or tune to the resonant frequency f0 with one tap.
- Electromagnetic Wave: Watch electric (red) and magnetic (blue) fields oscillate perpendicular to each other as they propagate. Adjust wavelength, amplitude and frequency; learn Maxwell's equations and c = lambda f.

Features:
- Clean, modern design (dark and light themes)
- Home screen organized by category
- Tips and a play button in the control panel
- Intuitive touch controls (tap, long press, drag) and parameter sliders
- An explanation sheet with formulas for every simulation
- In landscape, the canvas and control panel are shown side by side
- Supports larger text sizes
- 73 languages including English and Japanese, following your device language
- No sign-in: start exploring right away

Price:
- Free
- In-app purchases: none
- Subscriptions: none
- Ads: a banner ad by Pangle at the bottom of the screen

The "-raku" educational app series:
- SUUGAKU - Mathematics
- BUTURAKU - Mechanics
- DENRAKU - Electromagnetism
- HARAKU - Waves