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 gravity simulator, with magnetism in place of gravity.
You are in the Physics lab.
What the arrows, the readouts and the gyroradius–field graph are telling you.
On the circling particle the blue arrow is the velocity v and the red arrow is the magnetic force F = qv×B. They sit at a right angle to each other the whole way round: the force never speeds the particle up or slows it down, it only keeps swinging the velocity sideways. A constant-size push always at 90° to the motion is exactly what bends a straight path into a closed circle — the field marker ⊙ shows B pointing out of the page.
The dashed circle drawn through the particle is its cyclotron orbit, and the labeled radius line is the gyroradius r = m·v/(|q|·B). Slide the speed up and the circle widens; turn up the field strength B and it tightens. The companion graph plots that 1/B curve with your operating point marked, and the readouts confirm it — the cyclotron period T = 2π/B depends only on the field, not the speed, so a faster particle simply traces a bigger circle in the same time.
In uniform mode, turning up the electric field E shears the circle into a cycloid whose guiding center drifts sideways at speed E/B — the same for either charge sign. Switch to dipole mode and the electric slider hides: particles now spiral along the curved field lines and, where the field crowds together near a pole, the magnetic mirror reflects them so they bounce pole-to-pole and funnel inward — the mechanism that lights the aurora.
One force law — F = q(E + v×B) — pushed forward with a stable Boris integrator.
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 the speed |v| is conserved and circles stay closed instead of spiralling out.
In uniform-field mode B points out of the screen (the ⊙ markers). A charge loops in a circle whose gyroradius r = m·v/(|q|·B) matches the readout and the drawn radius line, turning the other way when you flip the charge sign. The period T = 2π·m/(|q|·B) is set by the field alone. Turn up the electric field and the loop shears into a cycloid, drifting at velocity E/B perpendicular to both fields.
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. For the full picture, with a whole stream of solar wind, the radiation belts and the real aurora colours, open the Aurora Simulator.
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Record how the path radius changes with speed and field strength, and how sign affects direction.
A magnetic field exerts F = qv×B, always perpendicular to the velocity, so a charge moving across the field circles with radius r = mv/(qB). Faster charges circle wider, stronger fields tighten the circle, and an angled entry gives a helix.
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