Electromagnetic Field
Move a charge. Watch its influence travel through space.
0.000c
Dashed amber shells: light-travel guides
Drag the glowing charge, or send a pulse to see a travelling disturbance.
Drag empty space to orbit · Shift/right-drag to pan · Scroll to zoom · Space pauses · Changing volume/slice/plane resets the experiment.
Description
A positive charge’s field does not receive instantaneous updates. This viewer calculates the electric and magnetic fields from the charge’s retarded position, velocity, and acceleration: the state whose signal has just had time to reach each vector. Acceleration produces a disturbance that travels outward at the model’s speed of light.
Instructions
- Move the charge: drag the glowing +. It follows the hollow target smoothly, limited to 0.45c. In 3D volume, dragging moves it on a screen-facing plane through its current position; orbit, then drag again to reach a different depth.
- Inspect a slice: switch to 2D slice and choose XY, XZ, or YZ. The grid and charge are restricted to that visible plane. You can still orbit and pan in 3D. Use Face plane if it becomes edge-on. The arrows retain all three components, so magnetic vectors may point out of the plane.
- See propagation: Send a pulse moves the charge to one side and back. Oscillate drives repeated motion; drag the charge to take over. Radiation E only isolates the acceleration term, making distant travelling waves easier to see. A resting charge has an electric field and no magnetic field.
- Read the arrows: cyan is E, purple is cB, and teal is the radiation-only electric term. Length and brightness compress magnitude so near and far vectors remain visible. A small circle with a dot or cross represents an arrow pointing approximately toward or away from you.
- Control the view: drag empty space to orbit, Shift/right-drag to pan, scroll to zoom. On the focused viewer, arrow keys orbit, Shift+arrows pan, +/− zoom, Home resets the camera, and Space pauses time. A/D move the charge on X, W/S on Y, Q/E on Z; the slice’s normal axis is locked. Pause freezes the charge and field while leaving the camera free.
Physics and model details
A causal field
For each sample point x at time t, the solver finds tᵣ from t − tᵣ = |x − r(tᵣ)| / c. With n pointing from the retarded charge position toward x, β = v/c, and κ = 1 − n·β, the field is:
+ n × [(n − β) × a]/(c²κ³R)
B = n × E / c
The first electric term falls as 1/R² and the acceleration term as 1/R. All source quantities are evaluated at retarded time. The charge was stationary at the origin before the experiment began. Switching geometry or resetting starts that initial condition again.
What the slice means
The 2D mode is a cross-section of the same 3D vacuum field, not two-dimensional electrodynamics. Its sample positions lie on one plane; vectors are not flattened onto that plane. Motion confined to a plane can produce a magnetic field normal to it.
Visible, slowed-down light
Distance, time, and charge strength use teaching units: c = 4 distance units per simulation second and q/(4πε₀) = 1. Multiply the purple magnetic vectors by c before comparing their lengths to E. Display gain changes only arrow rendering, not propagation or the fields. Vector lengths use a nonlinear magnitude compression and are not a linear quantitative scale.
The dashed amber circles/spheres are light-travel guides from recent drag or demo starts. They are not electric field lines, wave crests, or a claim of isotropic radiation intensity. The actual radiation arrows depend on direction and can vanish along the acceleration axis.
Numerical scope
This is a prescribed point-charge trajectory and the vacuum Liénard–Wiechert solution, sampled on a bounded grid. It does not simulate materials, boundaries, many-body forces, or radiation reaction. Motion is integrated at 120 steps per simulation second with piecewise smooth trajectory interpolation. Points too close to the singular charge are omitted; the sphere size is illustrative. The displayed fields are numerical approximations, with no physical wall at the edge of the sample box.
Background: University of Virginia: Liénard–Wiechert fields and Feynman: electromagnetic radiation.