A magnetic field never speeds a charge up or slows it down — the force F = q·v×B pushes only sideways, so it bends the path into circles and helices. Launch a charge into a uniform field and watch it trace a perfect cyclotron circle whose gyroradius you can read off; add an electric field for the classic E×B drift. Then flip to dipole mode — an approximate slice of Earth's magnetic field — and see solar-wind particles spiral along the field lines and funnel to the poles, the physics behind the aurora. It's the same force-driven trajectory idea as our orbit simulator, with magnetism in place of gravity.
Fire particles · switch field mode · change the charge sign
Gyroradius150 px
Cyclotron period6.28
ModeUniform field
A magnetic field does no work — it can only steer. Because the magnetic force is always perpendicular to the velocity, it never changes a particle's speed; it just bends the trajectory into a circle of radius r = m·v/(|q|·B), or a helix when there is motion along the field. That single fact is why the field can't heat the solar wind but can cage it: Earth's dipole traps charged particles, bounces them between the poles by the magnetic-mirror effect, and funnels them into the upper atmosphere near the poles to paint the aurora.
How It Works
One force law — F = q(E + v×B) — pushed forward with a stable Boris integrator.
1
The Lorentz force
Every frame the particle feels F = q(E + v×B). The electric term acts along E; the magnetic term q·v×B acts at right angles to the velocity, so it turns the path without adding energy. We advance it with a Boris pusher, the standard scheme that rotates the velocity by the exact gyro-angle each step, so circles stay closed instead of spiralling out.
2
Cyclotron circles and E×B drift
In uniform-field mode the field points out of the screen (the ⊙ markers). A charge loops in a circle whose gyroradius r = m·v/(|q|·B) matches the readout, turning the other way if you flip the charge sign. Turn up the electric field and the loop shears into a cycloid, drifting at velocity E/B perpendicular to both fields.
3
The dipole and the aurora
Switch to dipole mode for an approximate slice of a planet's magnetic field. Particles spiral along the curved field lines and, as the field strengthens toward a pole, the magnetic mirror reflects them — so they bounce between the poles and funnel inward, lighting an aurora glow just as the solar wind does at Earth.
What is the Lorentz force?
The Lorentz force is the force a charged particle feels in electric and magnetic fields: F = q(E + v×B). The electric part qE pushes along the electric field, speeding the particle up or slowing it down. The magnetic part q·v×B always acts at right angles to the particle's velocity, so it turns the path without changing the speed. Together they govern every trajectory in this simulator.
Why does a charged particle move in a circle in a magnetic field, and what is the gyroradius?
Because the magnetic force q·v×B is always perpendicular to the velocity, it does no work and cannot change the particle's speed — it only bends the path. A constant-magnitude force at right angles to a constant-speed motion is exactly what produces a circle. The radius of that circle is the gyroradius r = m·v/(|q|·B): faster particles trace wider circles, stronger fields tighter ones, and the sense of rotation flips when the charge changes sign. The cyclotron period T = 2π·m/(|q|·B) is independent of the speed.
What is E×B drift?
When a uniform electric field is added at right angles to the magnetic field, the particle no longer traces a closed circle. Its guiding centre drifts sideways at a steady velocity of magnitude E/B, perpendicular to both fields, so the path becomes a cycloid. Remarkably the drift velocity is the same for positive and negative charges, because reversing the charge reverses both the electric push and the sense of gyration, and the two cancel.
How does this cause the aurora, and what is the magnetic mirror?
Earth's magnetic field is shaped roughly like a dipole, with field lines that crowd closer together toward the poles. A charged particle from the solar wind spirals along a field line; as it moves into the stronger field near a pole the spiral tightens and its forward motion is reflected — the magnetic-mirror effect — so it bounces back and forth between the poles. Where these trapped particles finally spill into the upper atmosphere near the poles they collide with air molecules and make them glow, which is the aurora. See the live aurora forecast for tonight's real conditions.