How are electric field lines drawn?

Field lines are traced by numerically integrating the local electric field vector using a 4th-order Runge-Kutta method. Starting points are placed symmetrically around each charge. Line density is proportional to field strength, and equipotential contours are calculated on a 2D grid using Coulomb's law summed over all charges.

How does the photoelectric simulation work?

Photons arrive at a metal surface with energy E = hf. If E exceeds the metal's work function φ, an electron is ejected with kinetic energy KE = hf − φ. Below the threshold frequency, no electrons are emitted regardless of intensity — Einstein's key insight that earned him the 1921 Nobel Prize.

What is the magnetic field simulation?

The magnetic field simulation visualises field lines around current-carrying wires using the Biot-Savart law: dB = (μ₀/4π)(I dl × r̂)/r². You can add, move, and toggle wires to see how superposition of fields produces complex patterns.

Electromagnetism — 3D Simulations

Maxwell's Equations (differential form)

The complete description of classical electromagnetism in four equations

∇ · E = ρ / ε₀

Gauss's Law (Electric)

Electric field lines originate from positive charges and terminate on negative charges. Net flux through a closed surface equals enclosed charge / ε₀.

∇ · B = 0

Gauss's Law (Magnetic)

Magnetic field lines have no sources or sinks — magnetic monopoles do not exist. Every field line is a closed loop.

∇ × E = −∂B/∂t

Faraday's Law

A changing magnetic field induces a curling electric field. The basis of electric generators and inductors.

∇ × B = μ₀(J + ε₀ ∂E/∂t)

Ampère–Maxwell Law

Current and a changing electric field both produce curling magnetic fields. The displacement current term (ε₀ ∂E/∂t) unifies light as an EM wave.

Learning Resources

Articles and tutorials about the algorithms in this category

Article EM Wave Equation in 2D Finite-difference time-domain (FDTD) method for Maxwell's equations. Perfectly matched layer absorbers. → Article Coulomb's Law & Electric Fields Barnes-Hut tree for fast N-body Coulomb interaction. Field-line integration and equipotential surfaces. → Article Faraday Induction & Plasma Lenz's law in simulation. MHD pinch instabilities and plasma oscillation frequency. →

All articles →

About Electromagnetism Simulations

Electric fields, magnetic force, circuits, and Maxwell equations — live

Electromagnetism simulations visualise the fields and forces that govern electricity, magnetism, and light. Electric field-line plotters compute Coulomb-force vector fields from user-placed point charges and draw smooth field lines and equipotential surfaces. Magnetic field visualisers show solenoid and toroid flux patterns computed from Biot–Savart integration.

Circuit simulations model resistors, capacitors, and inductors with nodal analysis, animating charge flow and component voltages in real time. Electromagnetic wave animations show coupled oscillating E and B fields propagating at the speed of light. These interactive models cover the core content of a university electromagnetism course — Gauss's law, Faraday's law, Ampère's law — making abstract vector fields concrete and explorable.

Electromagnetism is arguably the most consequential branch of physics for modern technology: every electric motor, generator, radio transmitter, and semiconductor device operates through electromagnetic principles. Maxwell's four equations, unified in 1865, predicted the existence of electromagnetic waves and set the stage for special relativity. These interactive simulations make the invisible fields of charges and currents directly visible, building the intuition that underpins electrical engineering and photonics.

Key Concepts

Topics and algorithms you'll explore in this category

Coulomb's LawF = kq₁q₂/r² — electrostatic force between charges

Biot-Savart LawMagnetic field from current-carrying wires

Maxwell's EquationsUnified description of electric and magnetic fields

Photoelectric EffectEinstein's photon model of light-matter interaction

Field Line TracingRunge-Kutta integration along field gradients

Equipotential SurfacesContours of constant electric potential

⚡ Test Your Electromagnetism Knowledge

5 questions — Coulomb, Faraday, Maxwell, and more

Frequently Asked Questions

Common questions about this simulation category

How are electric field lines drawn?: Field lines are traced by numerically integrating the local electric field vector using a 4th-order Runge-Kutta method. Starting points are placed symmetrically around each charge. Line density is proportional to field strength, and equipotential contours are calculated on a 2D grid using Coulomb's law summed over all charges.
How does the photoelectric simulation work?: Photons arrive at a metal surface with energy E = hf. If E exceeds the metal's work function φ, an electron is ejected with kinetic energy KE = hf − φ. Below the threshold frequency, no electrons are emitted regardless of intensity — Einstein's key insight that earned him the 1921 Nobel Prize.
What is the magnetic field simulation?: The magnetic field simulation visualises field lines around current-carrying wires using the Biot-Savart law: dB = (μ₀/4π)(I dl × r̂)/r². You can add, move, and toggle wires to see how superposition of fields produces complex patterns.

Electromagnetism Simulations