Illustrated Physics
physics, drawn
Concept

Cyclotron motion — where it appears

The circling of a charged particle about a magnetic field, at the angular frequency qB/m for a slow particle, whatever its speed. Its radius grows with speed; its period does not, which is what a cyclotron exploits and what quantises into Landau levels.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Every path a rolling ball can take on a turntable, seen from the room. The paths, seen from the room, of four solid balls rolling without slipping on a turntable of radius 15 cm turning at 33.3 revolutions a minute (grey disc), over 6.3 seconds. A ball set down at rest relative to the room stays exactly where it is, spinning on the spot while the table turns under it. Every other ball moves on a circle, turning the same way as the table at 2/7 of its rate — once every 3.5 turns of the table — and comes back to where it started, whatever the push. A ball set down moving with the table does not ride with it: it circles on a path three and a half times the radius it started at, and the circle's centre is on the other side of the axis.

The ball a turntable will not throw off

Set a marble down on a spinning turntable and the expectation is that it will be flung off the edge. It is not. Placed at rest relative to the room, it stays exactly where it is, spinning on the spot while the table turns beneath it. Given a push, it moves in a circle, turning the same way as the table at two-sevenths of the table's rate, and comes back to where it started. Tilt the turntable and the marble does not roll downhill: it wanders across the slope in a chain of loops. A rolling ball on a rotating surface obeys exactly the equation of an electric charge in a magnetic field, and the two-sevenths is how much of every push goes into turning the ball rather than moving it.

mechanics · Circular motion Electrons that reach the anode, and electrons that turn back. Paths of electrons leaving a cathode 4 mm across at rest, in a cylindrical diode with an anode 8 mm across held at 4000 V, with no space charge, for axial magnetic fields of 0.80, 0.98, 1.02 and 1.30 times Hull's cut-off field of 142.2 millitesla; computed by integrating the Lorentz force. Below the cut-off the field only bends the path, and the electron still reaches the anode — at 0.98 of the cut-off it arrives almost tangentially. Just above it the electron turns back just short of the anode and returns to the cathode, then repeats the arc further round; at 1.30 times the cut-off it turns back well inside. Nothing reaches the anode, and the current stops completely within a few per cent of the field.

The field at which no electron reaches the anode

Put a hot wire inside a metal tube, make the tube positive, and electrons stream across from wire to tube. Add a magnetic field along the axis and they curve on the way, and still arrive — until, at one definite field, every one of them turns back a hair's breadth short of the tube and the current stops dead. The field at which it happens can be found without knowing anything about how the voltage is distributed between the wire and the tube, because one quantity the electron carries is fixed by the magnetic field alone. The microwave oven runs just inside that line.

electromagnetism · Magnetism

Named alongside it

The objects these essays reach for when they reach for this one.

Angular momentumCanonical momentumConstraintCoriolis forceDriftE cross b driftFrictionThe Lorentz forceMagnetronMoment of inertiaRollingRotating frame

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